GraphMatching.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/padath314/NetworkX-contribution/blob/main/GraphMatching.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Graph Matching"
      ],
      "metadata": {
        "id": "fx0-wxdulguU"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sJrRupdFAxDr"
      },
      "outputs": [],
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "A matching in a graph refers to a set of edges that do not share any common vertices with each other. This means that for any two edges in the matching, they are not connected to the same vertex."
      ],
      "metadata": {
        "id": "TifXcdROmog9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let us consider a scenario of a summer camp. There is a group of students who are to be made into teams of two. Students who are willing to be teamed up together can only be paired.\n",
        "\n",
        "Imagine we have the following students:\n",
        "\n",
        "- Alice\n",
        "- Bob\n",
        "- Charlie\n",
        "- Dave\n",
        "- Emily\n",
        "- Freddie\n",
        "- Grace\n",
        "\n",
        "Now, let's assume that the students have the following preferences for teaming up:\n",
        "\n",
        "- Alice is willing to team up with Bob, Dave, and Emily.\n",
        "- Bob is willing to team up with Alice, Charlie, Grace, and Emily.\n",
        "- Charlie is willing to team up with Bob, Emily, and Freddie.\n",
        "- Dave is willing to team up with Alice and Bob.\n",
        "- Emily is willing to team up with Charlie, Alice, and Dave.\n",
        "- Freddie is willing to team up with Grace and Charlie.\n",
        "- Grace is willing to team up with Bob, Freddie, and Alice.\n",
        "\n",
        "In terms of graph representation, we can visualize the preferences as follows:\n",
        "\n"
      ],
      "metadata": {
        "id": "We7mshq5nEL4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create an empty graph\n",
        "G = nx.Graph()\n",
        "\n",
        "preferences = {\n",
        "    'Alice': ['Bob', 'Dave', 'Emily'],\n",
        "    'Bob': ['Alice', 'Charlie', 'Grace', 'Emily'],\n",
        "    'Charlie': ['Bob', 'Emily', 'Freddie'],\n",
        "    'Dave': ['Alice', 'Bob'],\n",
        "    'Emily': ['Charlie', 'Alice', 'Dave'],\n",
        "    'Freddie': ['Grace', 'Charlie'],\n",
        "    'Grace': ['Bob', 'Freddie', 'Alice']\n",
        "}\n",
        "\n",
        "V = set(preferences.keys())\n",
        "E = set((student, teammate) for student, teammates in preferences.items() for teammate in teammates)\n",
        "\n",
        "G.add_nodes_from(V)\n",
        "G.add_edges_from(E)\n",
        "\n",
        "# Visualize the graph\n",
        "pos = nx.planar_layout(G)\n",
        "nx.draw_networkx(G, pos, with_labels=True, node_color='lightblue', node_size=1000, font_size=10)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "wy_YyJd2pEqc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        },
        "outputId": "10bc3a62-c2ab-42c0-cd05-87b7d97dba88"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this scenario, a matching would be the edges that represent the pairings we choose. Since a student cannot be part of more than one team, no vertex will be part of more than one edge in the matching."
      ],
      "metadata": {
        "id": "F5JkvC8dlcDW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's try creating a matching and check if it is valid:\n",
        "\n",
        "Matching: (Alice, Dave), (Emily, Bob), (Grace, Freddie)\n",
        "\n",
        "To check if this matching is valid, we need to ensure that no student is paired with more than one partner and that all pairs are mutually willing. Let's verify:\n",
        "\n",
        "- Alice is matched with Dave, which is one of her preferred partners.\n",
        "- Emily is matched with Bob, which is one of her preferred partners.\n",
        "- Grace is matched with Freddie, which is one of her preferred partners.\n",
        "\n",
        "So, this matching is valid since all students are paired with their preferred partners, and no student is paired with more than one partner.\n",
        "\n",
        "Now, let us confitm this result with the networkx module."
      ],
      "metadata": {
        "id": "9ooAc-Pf0TED"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Define the matching\n",
        "matching_1 = [('Alice', 'Dave'), ('Emily', 'Bob'), ('Grace', 'Freddie')]\n",
        "\n",
        "# Check if the matching is valid\n",
        "is_valid_matching = nx.is_matching(G, matching_1)\n",
        "\n",
        "# Print the result\n",
        "if is_valid_matching:\n",
        "    print(\"The matching is valid.\")\n",
        "else:\n",
        "    print(\"The matching is not valid.\")\n",
        "\n",
        "matching_graph_1 = G.edge_subgraph(matching_1)\n",
        "nx.draw_networkx(G, pos, with_labels=True, node_color='lightblue', node_size=1000, font_size=10)\n",
        "nx.draw_networkx_edges(matching_graph_1, pos,  width=3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        },
        "id": "4h7nLNsXpH56",
        "outputId": "e4f394a0-056e-4b24-c794-e78bb4af9bb3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The matching is valid.\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.LineCollection at 0x7de5147423b0>"
            ]
          },
          "metadata": {},
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, let's try another matching:\n",
        "\n",
        "Matching: (Alice, Grace), (Freddie, Charlie), (Charlie, Bob), (Bob, Emily), (Emily, Dave)\n",
        "\n",
        "This matching violates the condition of no student being paired with more than one partner:\n",
        "\n",
        "- Alice is paired with Grace, but Alice prefers Dave as her partner.\n",
        "- Freddie is paired with Charlie, but Freddie prefers Grace as his partner.\n",
        "- Charlie is paired with Bob, but Charlie prefers Emily as his partner.\n",
        "- Bob is paired with Emily, but Bob prefers Grace as his partner.\n",
        "- Emily is paired with Dave, but Emily prefers Charlie as her partner.\n",
        "\n",
        "Therefore, this matching is not valid.\n",
        "\n",
        "Again, rechecking the result."
      ],
      "metadata": {
        "id": "quDDP85x12Ht"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Define the second matching\n",
        "matching_2 = [('Alice', 'Grace'), ('Freddie', 'Charlie'), ('Charlie', 'Bob'), ('Bob', 'Emily'), ('Emily', 'Dave')]\n",
        "\n",
        "# Check if the matching is valid\n",
        "is_valid_matching = nx.is_matching(G, matching_2)\n",
        "\n",
        "# Print the result\n",
        "if is_valid_matching:\n",
        "    print(\"The matching is valid.\")\n",
        "else:\n",
        "    print(\"The matching is not valid.\")\n",
        "\n",
        "\n",
        "matching_graph_2 = G.edge_subgraph(matching_2)\n",
        "nx.draw_networkx(G, pos, with_labels=True, node_color='lightblue', node_size=1000, font_size=10)\n",
        "nx.draw_networkx_edges(matching_graph_2, pos,  width=3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        },
        "id": "jUZCf7ts2aOq",
        "outputId": "9efb2205-bc98-45e5-de3d-38d2221acc08"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The matching is not valid.\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.LineCollection at 0x7de5147ecf10>"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Augmenting paths\n",
        "\n",
        "Let G = (V, E) be a graph and M be a matching in G\n",
        "\n",
        "- A vertex v is **exposed** if no edge of M is incident with v.\n",
        "- A path in G is **alternating** if its edges alternate between being in M and not being in M (or vice versa).\n",
        "- An alternating path in G is an **augmenting path** if it starts at one exposed vertex and ends at a different exposed vertex.\n",
        "\n",
        "The number of unmatched edges in an augmenting path is one more than the number of matched edges, which means the total number of edges in an augmenting path is odd. To be more specific, an augmenting path starts at a vertex that is not matched (exposed). The path continues by alternately traversing edges that are either in the matching or not in the matching. Finally, the path ends at a different vertex that is also not matched (exposed).\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "UTAgc9aL6nKY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# code to demonstrate augmenting paths\n",
        "\n",
        "# Create an empty graph\n",
        "H = nx.Graph()\n",
        "\n",
        "# Add nodes to the graph\n",
        "H.add_nodes_from([1, 2, 3, 4, 5, 6])\n",
        "\n",
        "# Add edges to the graph\n",
        "H.add_edges_from([(1, 2), (1, 3), (2, 3), (2, 4), (3, 6), (4, 5), (5, 6)])\n",
        "\n",
        "# Visualize the graph\n",
        "pos = nx.planar_layout(H)\n",
        "\n",
        "# Find a non-maximal matching\n",
        "non_maximal_matching = [(1, 2), (4, 5)]\n",
        "matching_graph = H.edge_subgraph(non_maximal_matching)\n",
        "\n",
        "# Finding the augmenting path\n",
        "augmenting_path = [(3, 1), (1, 2), (2, 4), (4, 5), (5, 6)]\n",
        "aug_path_graph = H.edge_subgraph(augmenting_path)\n",
        "nx.draw_networkx_edges(aug_path_graph, pos, edge_color='yellow',  width=5 )\n",
        "\n",
        "nx.draw_networkx(H, pos, with_labels=True,node_color='lightblue', node_size=1000, font_size=10)\n",
        "nx.draw_networkx_edges(matching_graph, pos, edge_color='red', width=2 )\n",
        "\n",
        "caption = \"The matched edges are shown in red and the yellow edges are part of the augmenting path. \"\n",
        "plt.figtext(0.5, 0.01, caption, wrap=True, horizontalalignment='center', fontsize=10)\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        },
        "id": "jgKXxjLp8f2G",
        "outputId": "db8a6b94-1ee3-4f0a-9fee-279bb3afa5f3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The augmenting path is 3-1-2-4-5-6 is highlighted in the above picture.\n",
        "\n",
        "A **matching augmentation** is the process of improving a matching in a graph by finding an augmenting path.\n",
        "\n",
        "To perform matching augmentation of a matching M in a graph G, follow these steps:\n",
        "\n",
        "1. Find an augmenting path for M in G.\n",
        "2. If an augmenting path P is found, modify the matching M:\n",
        "   - Add unmatched edges in the augmenting path P to the matching M,\n",
        "   - Remove matched edges in the augmenting path P from M\n",
        "   - This can also be considered as the symmetric difference between the matching and the augmenting path edges.\n",
        "5. Repeat until no more augmenting paths can be found.\n",
        "\n",
        "By iteratively finding augmenting paths and updating the matching, the process gradually improves the matching, increasing the number of matched vertices. Infact, by Berge's Lemma, which will be described later, this process will terminate in an optimal matching.\n",
        "\n"
      ],
      "metadata": {
        "id": "g86p8a2YtdIz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# code that does augmentation in the above graph\n",
        "\n",
        "new_matching = list(non_maximal_matching)\n",
        "\n",
        "for edge in augmenting_path:\n",
        "  if edge not in non_maximal_matching:\n",
        "    new_matching.append(edge)\n",
        "  else:\n",
        "    new_matching.remove(edge)\n",
        "\n",
        "# Create a new graph for the updated matching\n",
        "updated_matching_graph = nx.Graph()\n",
        "updated_matching_graph.add_edges_from(new_matching)\n",
        "\n",
        "# Visualize the updated matching\n",
        "nx.draw_networkx(H, pos, with_labels=True, node_color='lightblue', node_size=1000, font_size=10)\n",
        "nx.draw_networkx_edges(updated_matching_graph, pos, width=3)\n",
        "plt.title(\"Updated Matching (After Augmentation)\")\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "bR72famTutOq",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 428
        },
        "outputId": "257f792c-9b63-4d50-b511-164c5c995de0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "No more augmentation paths can be found."
      ],
      "metadata": {
        "id": "wOiPVu-1bMyq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "### Berge's Lemma\n",
        "By Berge's lemma, matching M is maximum if and only if there is no M-augmenting path in G. Hence, every matching is either maximum, or can be augmented further. Thus, starting from an initial matching, we can compute a maximum matching by augmenting the current matching with augmenting paths as long as we can find them, and return whenever no augmenting paths are left."
      ],
      "metadata": {
        "id": "d4SM7qm38pgp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## [Blossom Algorithm](https://en.wikipedia.org/wiki/Blossom_algorithm)\n",
        "\n",
        "Let's see how we can find maximal matchings in a graph using the Blossom algorithm, developed by Jack Edmonds.\n",
        "\n",
        "The Blossom algorithm is a graph matching algorithm that can efficiently find a maximal matching in a graph. It works by iteratively finding augmenting paths in the graph and using them to improve the matching. The algorithm is based on the concept of blossoms, which are subgraphs that capture the structure of the graph and help in finding augmenting paths.\n",
        "\n",
        "The Blossom algorithm has a time complexity of O(V<sup>3</sup>), where V is the number of vertices in the graph. This makes it a polynomial-time algorithm, which is significant because it guarantees efficient solutions for graphs of practical size.\n",
        "\n",
        "## Blossoms and Contractions\n",
        "\n",
        "### Blossoms\n",
        "\n",
        "Given a graph G and a matching M on it, a *blossom* refers to an odd-length cycle in G consisting of 2k+1 edges, with exactly k edges belonging to M. Within the blossom, there exists a special vertex called the *base*, which is not incident to any of the k matched edges in the cycle. This base vertex, v, has a *stem*, which is an alternating path of even length leading from v to an exposed vertex, denoted by w.\n",
        "\n",
        "Blossoms play a crucial role in Edmond's matching algorithms. Once the algorithm finds a blossom, it is contracted to a single vertex and the algorithm continues searching for an augmenting path iteratively in the contracted graph.\n",
        "\n",
        "### Finding Blossoms\n",
        "\n",
        "1. Start from an exposed vertex v in the graph and label the starting vertex as an outer vertex (o).\n",
        "2. Traverse the graph in an alternating fashion, that is picking edges from outside the matching and inside the matching at alternate levels of the resulting tree.\n",
        "3. Label the vertices that are at an even distance from v as outer (o) and at an odd distance as inner (i).\n",
        "4. If we find an edge between two outer vertices, then we have found an odd-length cycle, indicating the presence of a blossom."
      ],
      "metadata": {
        "id": "ncRFuqJG8T11"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### A blossom in a graph G1 with a matchign M1"
      ],
      "metadata": {
        "id": "vfyxMPmFSOtW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create an empty graph\n",
        "G1 = nx.Graph()\n",
        "\n",
        "# Add nodes to the graph\n",
        "G1.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
        "\n",
        "# Add edges to the graph\n",
        "G1.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (9, 5)])\n",
        "\n",
        "# Matching\n",
        "M1 = [(2, 3), (4, 5), (6, 7), (8, 9)]\n",
        "\n",
        "# Visualize the graph\n",
        "pos1 = nx.shell_layout(G1)\n",
        "\n",
        "# Blossom B\n",
        "blossom_edges = [(5, 6), (6, 7), (7, 8), (8, 9), (9, 5)]\n",
        "\n",
        "nx.draw_networkx_edges(G1, pos1, blossom_edges, edge_color='green',width=6)\n",
        "nx.draw_networkx(G1, pos1, with_labels=True, node_color='lightblue', node_size=800, font_size=10)\n",
        "nx.draw_networkx_edges(G1, pos1, M1,width=2.5)\n",
        "nx.draw_networkx_nodes(G1, pos1, nodelist=[1], node_color='red')\n",
        "\n",
        "plt.figtext(0.5, 0.01, \"The blossom is highlighted in green, '1' is the exposed vertex at the end of the stem.\", wrap=True, horizontalalignment='center', fontsize=10)\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "z1HOnYXt5c8o",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457
        },
        "outputId": "4fc1047d-43ef-4983-9b16-0e3145f1c76b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "After the blossom is contracted to a single vertex, the contracted graph G2 will like look like this."
      ],
      "metadata": {
        "id": "eJS_lGv9aaxX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create an empty graph\n",
        "G2 = nx.Graph()\n",
        "\n",
        "# Add nodes to the graph\n",
        "G2.add_nodes_from([1, 2, 3, 4, 5])\n",
        "\n",
        "# Add edges to the graph\n",
        "G2.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 5)])\n",
        "\n",
        "# Matching\n",
        "M2 = [(2, 3), (4, 5)]\n",
        "\n",
        "nx.draw_networkx(G2, pos1, with_labels=True, node_color='lightblue', node_size=800, font_size=10)\n",
        "nx.draw_networkx_edges(G2, pos1, M2,width=2.5)\n",
        "nx.draw_networkx_nodes(G2, pos1, nodelist=[1], node_color='red')\n",
        "nx.draw_networkx_nodes(G2, pos1, nodelist=[5], node_color='green')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        },
        "id": "X40WY2a7g7-z",
        "outputId": "480fef59-e26c-42d1-dd8c-a65c131dc452"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "An M2-augmenting path (referred to as P2) exists in G2 if and only if there is an M1-augmenting path in G1. Moreover, this M2-augmenting path (P2) can be elevated to an M1-augmenting path by extending the blossom, such that the section of the path that passes through the contracted vertex (5, in this case) is substituted with a suitable segment traversing through the blossom, denoted as B.\n",
        "\n",
        "*Case 1*\n",
        "\n",
        "When the augmenting path P2 travels through a segment, let's say `u --> (b) --> w` in G2( `b` being the contracted blossom vertex ), we transform this segment into `u --> (u' --> .. --> w') --> w` in G1. Here, the vertices `u'` and `w'` belong to the blossom B's side, `(u'->..->w')`, and their selection ensures that the path's alternating pattern is preserved."
      ],
      "metadata": {
        "id": "htRP2in_SIkQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "B1 = nx.Graph()\n",
        "B1.add_edges_from([('x1', 'x2'), ('x2', 'x3'), ('x3', 'u'), ('u', 'b'), ('b', 'w'), ('w', 'y1'), ('y1', 'y2')])\n",
        "M1 = [('x2', 'x3'), ('u', 'b'), ('w', 'y1')]\n",
        "exposed_vertices_1 = ['x1', 'y2']\n",
        "pos_b1 = {node: (2 * i, 1) for i, node in enumerate(B1.nodes)}\n",
        "aug_path_1 = [('x1', 'x2'), ('x2', 'x3'), ('x3', 'u'), ('u', 'b'), ('b', 'w'), ('w', 'y1'), ('y1', 'y2')]\n",
        "\n",
        "B2 = nx.Graph()\n",
        "edges = [('x1', 'x2'), ('x2', 'x3'), ('x3', 'u'), ('u', \"u'\"), (\"u'\", \"v'\"), (\"v'\", \"w'\"), (\"w'\", 'w'),\n",
        "         (\"u'\", \"x'\"), (\"x'\", \"y'\"), (\"y'\", \"w'\"), ('w', 'y1'), ('y1', 'y2')]\n",
        "B2.add_edges_from(edges)\n",
        "M2 = [('x2', 'x3'), ('u', \"u'\"), ('w', 'y1'), (\"x'\", \"y'\"), (\"v'\", \"w'\")]\n",
        "pos_b2 = nx.spring_layout(B2)\n",
        "b1_nodes = ['x1', 'x2', 'x3', 'u', 'w', 'y1', 'y2']\n",
        "aug_path_2 = [('x1', 'x2'), ('x2', 'x3'), ('x3', 'u'), ('u', \"u'\"), (\"u'\", \"v'\"), (\"v'\", \"w'\"), (\"w'\", 'w'), ('w', 'y1'), ('y1', 'y2')]\n",
        "\n",
        "for node in b1_nodes:\n",
        "    pos_b2[node] = pos_b1[node]\n",
        "\n",
        "pos_b2['w'] = (14, 1)\n",
        "pos_b2['y1'] = (16, 1)\n",
        "pos_b2['y2'] = (18, 1)\n",
        "pos_b2[\"u'\"] = (8, 1)\n",
        "pos_b2[\"w'\"] = (12, 1)\n",
        "pos_b2[\"v'\"] = (10, 1.05)\n",
        "pos_b2[\"x'\"] = (9, 0.95)\n",
        "pos_b2[\"y'\"] = (11, 0.95)\n",
        "\n",
        "# Create subplots and display both figures side by side\n",
        "plt.figure(figsize=(12, 5))\n",
        "\n",
        "plt.subplot(1, 2, 1)\n",
        "nx.draw_networkx_edges(B1, pos_b1, aug_path_1, edge_color='yellow',  width=5 )\n",
        "nx.draw_networkx_nodes(B1, pos_b1, exposed_vertices_1, node_color='red', node_size=600)\n",
        "nx.draw_networkx(B1, pos_b1, with_labels=True, node_color='lightblue', node_size=500, font_size=10)\n",
        "nx.draw_networkx_nodes(B1, pos_b1, nodelist=['b'], node_color='green')\n",
        "nx.draw_networkx_edges(B1, pos_b1, M1, width=3)\n",
        "plt.title(\"Figure 1\")\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "nx.draw_networkx_edges(B2, pos_b2, aug_path_2, edge_color='yellow',  width=5 )\n",
        "nx.draw_networkx_nodes(B2, pos_b2, exposed_vertices_1, node_color='red', node_size=600)\n",
        "nx.draw_networkx(B2, pos_b2, with_labels=True, node_color='lightblue', node_size=500, font_size=10)\n",
        "nx.draw_networkx_nodes(B2, pos_b2, nodelist=[\"u'\", \"v'\", \"w'\", \"y'\", \"x'\"], node_color='green')\n",
        "nx.draw_networkx_edges(B2, pos_b2, M2, width=3)\n",
        "plt.title(\"Figure 2\")\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "id": "oGemeN1tqqTM",
        "outputId": "313308e9-66b5-418e-a6e8-e930cfc7c27c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here the alternating path after lifting is `x1 - x2 - x3 - u - u' - v' - w' - w - y1 - y2`. It cannot be `u' - x' - y' - w'` as it is not an alternating path ( the edges `y'w'` and `w'w` are not in the matching )"
      ],
      "metadata": {
        "id": "21xBhGLKv6CZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "*Case 2*\n",
        "\n",
        "In the scenario where the augmenting path P2 terminates at vertex b, the corresponding path segment u -> b in G2 is updated to u -> (u' -> ... -> w') in G1. Here, the choice of vertices u' to w' forms a segment within the blossom B, such that the path retains its alternating sequence. This transformation in G1 reflects the nature of the augmenting path's termination at vertex b in G2."
      ],
      "metadata": {
        "id": "485AxJ1FBFrm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a graph B3\n",
        "B3 = nx.Graph()\n",
        "B3.add_edges_from([('x1', 'x2'), ('x2', 'x3'), ('x3', 'x4'), ('x4', 'u'), ('u', 'b')])\n",
        "M3 = [('x2', 'x3'), ('x4', 'u')]\n",
        "exposed_vertices_3 = ['x1', 'b']\n",
        "pos_b3 = {node: (2 * i, 1) for i, node in enumerate(B3.nodes)}\n",
        "aug_path_3 = [('x1', 'x2'), ('x2', 'x3'), ('x3', 'x4'), ('x4', 'u'), ('u', 'b')]\n",
        "\n",
        "# Create a graph B4\n",
        "B4 = nx.Graph()\n",
        "edges = [('x1', 'x2'), ('x2', 'x3'), ('x3', 'x4'), ('x4', 'u'), ('u', \"u'\"), (\"u'\", \"v'\"), (\"v'\", \"w'\"), (\"u'\", \"x'\"), (\"x'\", \"y'\"), (\"y'\", \"w'\")]\n",
        "B4.add_edges_from(edges)\n",
        "M4 = [('x2', 'x3'), ('x4', 'u'), (\"u'\", \"v'\"), (\"x'\", \"y'\")]\n",
        "pos_b4 = nx.spring_layout(B4)\n",
        "b3_nodes = ['x1', 'x2', 'x3', 'x4', 'u']\n",
        "aug_path_4 = [('x1', 'x2'), ('x2', 'x3'), ('x3', 'x4'), ('x4', 'u'), ('u', \"u'\"), (\"u'\", \"v'\"), (\"v'\", \"w'\")]\n",
        "\n",
        "# Create a graph B5\n",
        "B5 = nx.Graph()\n",
        "edges = [('x1', 'x2'), ('x2', 'x3'), ('x3', 'x4'), ('x4', 'u'), ('u', \"u'\"), (\"u'\", \"v'\"), (\"v'\", \"w'\"), (\"u'\", \"x'\"), (\"x'\", \"y'\"), (\"y'\", \"w'\")]\n",
        "B5.add_edges_from(edges)\n",
        "M5 = [('x2', 'x3'), ('x4', 'u'), (\"v'\", \"w'\"), (\"x'\", \"y'\")]\n",
        "aug_path_5 = [('x1', 'x2'), ('x2', 'x3'), ('x3', 'x4'), ('x4', 'u'), ('u', \"u'\")]\n",
        "\n",
        "\n",
        "for node in b3_nodes:\n",
        "    pos_b4[node] = pos_b3[node]\n",
        "\n",
        "pos_b4[\"u'\"] = (10, 1)\n",
        "pos_b4[\"w'\"] = (14, 1)\n",
        "pos_b4[\"v'\"] = (12, 1.05)\n",
        "pos_b4[\"x'\"] = (11, 0.95)\n",
        "pos_b4[\"y'\"] = (13, 0.95)\n",
        "\n",
        "exposed_vertices_4 = [\"x1\", \"w'\"]\n",
        "\n",
        "# Create subplots and display both sets of figures side by side\n",
        "plt.figure(figsize=(12, 5))\n",
        "\n",
        "# First subplot for B3\n",
        "plt.subplot(1, 3, 1)\n",
        "nx.draw_networkx_edges(B3, pos_b3, aug_path_3, edge_color='yellow',  width=5 )\n",
        "nx.draw_networkx_nodes(B3, pos_b3, exposed_vertices_3, node_color='red', node_size=600)\n",
        "nx.draw_networkx(B3, pos_b3, with_labels=True, node_color='lightblue', node_size=500, font_size=10)\n",
        "nx.draw_networkx_nodes(B3, pos_b3, nodelist=['b'], node_color='green')\n",
        "nx.draw_networkx_edges(B3, pos_b3, M3, width=3)\n",
        "plt.title(\"Figure 1\")\n",
        "\n",
        "# Second subplot for B4\n",
        "plt.subplot(1, 3, 2)\n",
        "nx.draw_networkx_edges(B4, pos_b4, aug_path_4, edge_color='yellow',  width=5 )\n",
        "nx.draw_networkx_nodes(B4, pos_b4, exposed_vertices_4, node_color='red', node_size=600)\n",
        "nx.draw_networkx(B4, pos_b4, with_labels=True, node_color='lightblue', node_size=500, font_size=10)\n",
        "nx.draw_networkx_nodes(B4, pos_b4, nodelist=[\"u'\", \"v'\", \"w'\", \"y'\", \"x'\"], node_color='green')\n",
        "nx.draw_networkx_edges(B4, pos_b4, M4, width=3)\n",
        "plt.title(\"Figure 2\")\n",
        "\n",
        "# Third subplot for B5\n",
        "plt.subplot(1, 3, 3)\n",
        "nx.draw_networkx_edges(B5, pos_b4, aug_path_5, edge_color='yellow',  width=5 )\n",
        "nx.draw_networkx_nodes(B5, pos_b4,[\"u'\"], node_color='red', node_size=600)\n",
        "nx.draw_networkx(B5, pos_b4, with_labels=True, node_color='lightblue', node_size=500, font_size=10)\n",
        "nx.draw_networkx_nodes(B5, pos_b4, nodelist=[\"u'\", \"v'\", \"w'\", \"y'\", \"x'\"], node_color='green')\n",
        "nx.draw_networkx_edges(B5, pos_b4, M5, width=3)\n",
        "plt.title(\"Figure 3\")\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "id": "hwj2GuRNrvsc",
        "outputId": "a6318679-81a7-482c-9bb3-0bc8aea31dd0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x500 with 3 Axes>"
            ],
            "image/png": 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9F/gOBYrHfkJI0iIlvvW+IGmapFmZbXPgdgZuHwDgTuQK9+KXUgAAAPCs0mBQyVP9GRVzJaVx4t+gxLffzyvjb74l4+p2ElsqDY5w9SYAgGuQK9yLohQAAAA8q6o01LcyyIRQuWoq6sZ+0lwlFrI9r4wHGjMqwpoQKpeUWCekqjSU2QsAAGxHrnAvilIAAADwrMEn+itmvlkBY4xvpAOSPibpc5KmpL+tgBHU8plvGnX7AAD3IVe4F0UpAAAAeFZlSZFCA9bquHXBexW38nOVo7gV020L7u27HQoYqixhiVYAcDtyhXtRlAIAAIBnBQxDc6vK+lYHqa1cqGU1G8f+Bjzj7QS1rGaj5lReIymxRsi8qjIFDBavBQC3I1e4F0UpAAAAeNq8qjINvNj2/Su/rqJAbqdKFAVCun/l1/tuW5LmVpXldBsAgPwhV7gTRSkAAAB4WlmoSPWVE/pu11TU6b7lX8zpNu5b/qWUhXHrKyeoLMR0DADwCnKFO1GUAgAAgOc1VE9SabD/1PaW+ffo3Q2fyMlr393wSd0y/+6+26XBgBqqJ+XktQEA9iFXuA9FKQAAAHheKBjQiplVKW13LvkLfWjl36k4WJrxuiEBI6jiYKk+tPIbeseSj6Tct2JmlUJBTqMBwGvIFe7DEQIAAIAv1JSXaNn01G+lb5l/jx6841k1TF8nSWMOOJL3N0xfpwfveDblW29JWjZ9kmrKS3IYNQDATuQKd2FyIwAAAHxj/uRySdLeM5f62moq6vTZN/5Qx9pf0zMHH9eeU7/V6Y4WKWXJW0MzKsJaPvNNum3BvX1XThpo2fRJfa8PAPAucoV7UJQCAACAr8yfXK6K4iLtPtWm7li8r722cqHuW/El3SepK9Kp0x1HFIn3KhQo1oyKuZoQGn4QUXp1ugffegOAf5Ar3IGiFAAAAHynprxEvze3WvvOXlJze6eseFxGoP/Ud0KoXHMnLx3x+YaishRUfWWZGqonsS4IAPhQaq7okqHU30WNnSsSj6+vnECuGCeOGAAAAHwpFAxo+YyLun3ezXrxtw/rcttFSZJlWYrHIuofelgyFJFlJW6HAhe1cMrDun3eT7R8BgvVAoCfJXJFlW6fV62FU8qlWDRxh2XJGPhAy1I00p8rOtrbNHdiiW6fV02uyAK/lAIAAICPmSoJnNA3//Zr6uj8e9UtXKT5Sxr03/7ies2sv06x+BwFAy+qNHhGP336RTX9ap+e+ckBBYyopD+U9CdO7wAAwAZloSItqZ6kJ//pG/rF757VU//3F2rviao7FlMsbsmKx/WDx76vg/v36tBL+3T0tQN65le/UtmsNzkduqdRlAIAAICPNWn/fqm9XZKiOvLyPh15eZ++948/0OzZn5D0dkkfkCS9PFn67E+l8+ek6mpJ2iQpLiYXAEDhMJue1dwZ0zVvmMXKP/azH2nHjh19t5uamvSmN1GUygYZFgAAAD5mqqkptWX+fGn2bEnaKGm5pDJJ0saNifs3b04+8oKkl+wIEgDgAt3d3dq+fbs2JhPCIIPbTdO0IyxfoygFAAAAnzoh6ZAGjxkSYwpD0jpJIUlrJUm1tVJ9vQY9ngEHABSKHTt2qLe3N+2i1LZt29TT02NHaL5FUQoAAAA+tUmWNbjIJDU2StINkiqvtvQPMjZupCgFAIXKNE1VVlaqoaFh2PvXr18vw+hf/ry7u1u7du2yKzxfoigFAAAAnzL16qvS2bOprYkvugd+251alHrhheQaVInXSL1AOADAr0zT1Pr16xUMBoe9f/Lkybr++uuHPAfjR1EKAAAAPmUO+ZXUnDmJKXqpRalVkoolJYpS8bi0dWvyvtOSDuY5TgCA0yKRiLZu3Tri1L0k1pXKLYpSAAAA8KFzkl4adj2pxMyLDQNaJ0i6WZK0YIE0Y4YGLY7OgAMA/G7Pnj3q7OzMuCi1ZcsWRaPRfIbmaxSlAAAA4EObZVmDi0vJqXuLJFUPenxikGEYrCsFAIXINE2VlZVp+fLloz5uw4YNKbcvX76svXv35jM0X6MoBQAAAB8y1dIiHT+e2pooSjUO8/jUdaV27pSuXOl/LQCAv5mmqTVr1qi4uHjUx9XU1Ojaa68d8lyMD0UpAAAA+NDQ9aSmTZOuu05KXU8qaY2kxMK2jY1SNCpt25a8r1nS0TzFCQBwWiwW06ZNm8acupfEulK5Q1EKAAAAPnNJ0vNprieVNFFSYsrG4sXSlCmDp/BtykegAAAX2L9/v9rb28ddlNq0aZPi8Xg+QvM9ilIAAADwmS2S4sMWpaR5kuaM8LzEICMQkDZsGFyUahr2GQAA7zNNU8XFxbr55pvTevzgotT58+f18ssv5yM036MoBQAAAJ8xdeqU9Prrqa2JMcRo34Knriv13HNSb2//awIA/Mk0Ta1atUoTJkxI6/F1dXUKh8NDXgOZoygFAAAAnxm6ntSkSdL110ujF6XW9/1r40apu1vatSvZ8qqk1pxGCQBwnmVZMk0z7al7SawrlRsUpQAAAOAjVyTtHFKUWr9eCgal0YtSUyQ1SJJuuEGqqGBdKQDwu9dee01nzpzJSVHKsqxchlYQKEoBAADAR7ZLigwpSjU2StIsJdaUGk1ikFFUJK1bN7goxbfgAOA3pmkqEAho7dq1GT2vMZFY+pw6dUqHDh3KZWgFgaIUAAAAfMTU+fPS/v2prf3rSRljPD91XanNm6VYrP+1AQD+Ypqmli9frokTJ2b0vAULFmjGjBlDXguZoSgFAAAAHzG1eXNqS1mZtHy5NPrUvaTUotTly9ILLyRbXpR0MRdBAgBcwLIsNTU1ZTx1T5IMw2BdqRygKAUAAACf6JX03JCpe2vWSMXFUnpFqRmSFkqSVq6USkoGTuGzJG3JUawAAKe1tLTo2LFj4ypKSSx2ngsUpQAAAOATuyV1DSlKJcYM0yQtTvN1EoOMkhJp9WrWlQIAv0oWkdavXz/GI4c3uCh15MgRHTt2LOu4CglFKQAAAPiEqcuXpT17UlsTY4YNGns9qb5n9P2rsVHatEmKx/u3AQDwB9M0tXTpUk2dOnVcz1+yZIkmT56c0rZpE1dqzQRFKQAAAPiEqa1bBxaQpFBIuvlmKb2pe0mp60qdPy8dOJBs2S2pI+tIAQDOM01z3FP3JCkQCGjDhg1DXhPpoygFAAAAH4hJ2jxk6t6qVdKECVJmRamwpDpJiel7RUUDp/BFJW3LMlYAgNNOnTql119/PauilDR0Cl9TU1NWr1doKEoBAADAB/ZKujTCelITJS3L8PUSg4zycummmwavK8WAAwC8LjnNLtdFqVdeeUVnzpzJ6jULCUUpAAAA+ICpri5px47U1sRYYb2kYIavlzqFzzQly+rfFgDA20zT1DXXXKOZM2dm9To33nijysvLU9pYVyp9FKUAAADgA6a2b5d6e/tbAgFp7Vops6l7SalFqZMnpcOHky3bJXWPO1IAgPOyXU8qqaioSOvWrRvy2kgPRSkAAAB4nCXJHDJ178YbpUmTpPEVpRZKmi5JWrdOMoyBU/h6JO0cZ6wAAKdduHBB+/bty0lRSho6hY+iVPooSgEAAMDjDkg6P6Qo1dgoSaWSbhrHaxpKFrOqqqRlywavK8WAAwC8avPmzZKyX08qqTGRcPrs3btXbW1tOXltv6MoBQAAAI8z1dsrbd2a2poYa6yRVDzO1+0fZCTXlRq4TQCAN5mmqdraWoXD4Zy83sqVK1VSUtJ327IsbdmyJSev7XcUpQAAAOBxpvbskbq6UlvXr5fGN3UvKXVdqcOHpePHky1bJEWzeG0AgFOampq0ceNGGYaRk9crKSnR6tWrU9qYwpceilIAAADwsOHXk1q6VJo6VcquKLVUUpUkacOGREv/djolPZ/FawMAnHD58mXt2bMnZ1P3klhXanwoSgEAAMDDjkg6MaQolRgbhCStHvqUtAUkJapR06dL113HFD4A8LqtW7cqHo/nvSi1a9cudXZ25nQbfkRRCgAAAB5mKhaTrq5Z2ycxNlgpqSzL1+8fZDQ2UpQCAK8zTVPV1dW69tprc/q6a9asUVFRUd/taDSqbdu25XQbfkRRCgAAAB5mat8+qb09tTUx3S4X34Knrit14IB05kyyZZOkeA62AQCwi2maOV1PKqm8vFwrVqxIaWtqasrpNvyIohQAAAA8rGnI1L0FC6RZs6TcFKVulFQuqX9dqf5fZV2UtD8H2wAA2KGrq0s7duzI+dS9JNaVyhxFKQAAAHjUcUmHR1hPKiBpbQ62Eep7ndpaae5cpvABgFft2LFDvb29amxszMvrDy5Kbdu2TT09PXnZll9QlAIAAIBHbZJlDS4SJYtSN0iqzNF2UqfwUZQCAG8yTVNVVVVaunRpXl5/3bp1KdMCe3p6tHPnzrxsyy8oSgEAAMCjTL3yinT2bGproiiVy6kZqUWpF14YuIaVKcnK4bYAAPlimqbWr1+vYDCYl9efPHmyrr/++iHbxMgoSgEAAMCjzCG/kqqtlerrpdwWpVZJKpGUKEpZlrRlS/K+Vkmv53BbAIB8iEQi2rp1a97Wk0oaPDWQotToKEoBAADAg85KennYqXuJmRPrc7itUkk3S5Lmz5dmzmQKHwB4zZ49e3TlypW8F6UGv/6WLVsUjUbzuk0voygFAAAAD9osy5IGX207MRZYLKk6x9tLDDIMg3WlAMCLTNNUWVmZli9fntftbEheqvWqjo4OvfDCC3ndppdRlAIAAIAHmWpulk6cSG3N/XpSfa+cso2dO6XOzv5YAADu1tTUpLVr1yoUCuV1O9OnT9d1112X0sYUvpFRlAIAAIAHDV1PqrpauvZaScrHpb7XSEosjLtxoxSNStu2Je9rufofAMCNYrGYNm/enPepe0mDt0NRamQUpQAAAOAx7ZJeGGU9qQ3DPCdbFZJWSJIWL5amTh08hW9THrYJAMiFffv2qb293bGi1KZNmxSPx23ZttdQlAIAAIDHbJUUH7YoJc2XNDtP200MMgIBacMG1pUCAK8wTVPFxcVatWqVLdsbXJS6cOGCXnrpJVu27TUUpQAAAOAxpk6elA4eTG3N33pSfVtI2da2bVJPT39MAAB3Mk1Tq1at0oQJE2zZXm1trerr64fEgKEoSgEAAMBjmrRp0Gy5ykqpoUHKb1FqvSRDUqIo1d0t7dqVvO9VSafzuG0AwHhYliXTNNXYmI/1BkfGulLpoSgFAAAAD7kiaeeQqXvr10vBoJTfotRkSQ2SpGXLpIkTWVcKANzu1Vdf1dmzZ21bTyppuKKUZVm2xuAFFKUAAADgIdskRdXUlNqaOPefLWlunrefGGQUFUnr1rGuFAC4nWmaCgaDWrNmja3bHVyUOn36tA4OnncOilIAAADwElPnzkmD14vtX0/KyPP2U9eV2rJFikb7YwMAuItpmlq+fLkmTpxo63YXLFigGTNmDIkFqShKAQAAwENMbd6c2lJWJq1YIeV36l5SalHq8mVp795kyz5JF2yIAQCQDsuy1NTUZPvUPUkyDGPIOlYUpYaiKAUAAACP6JX03JD1pNaulUIhyZ6iVI2kayVJN90klZYOnMJnSdpiQwwAgHS0tLTo+PHjjhSlJBY7TwdFKQAAAHjELkndQ4pSiXP+aZIW2RRHYpBRUiKtXs26UgDgVski0Pr16x3Z/uCiVHNzs44ePepILG5FUQoAAAAeYerSJen551NbE+f8G5T/9aT6tpiybdOU4vFkC0UpAHCLpqYmNTQ0aMqUKY5sf/HixUO2vWkTV2odiKIUAAAAPMLU1q0DC0BScbG0apUkNY70pDzoL0o1NkoXLkgvv5xs2S2pw8ZYAAAjMU3Tsal7khQIBLRhw4aUNqbwpaIoBQAAAA+ISdo8ZOreqlXShAmSPetJJdVJCktKTN8rKho4hS8m6TkbYwEADOfkyZM6ePCgo0UpaegUvqamJocicSeKUgAAAPCAvZIuj7Ce1CRJ19scT2KQUVYmrVzJulIA4DbJaXKDf6lkt8FFqVdffVWtra0OReM+FKUAAADgAU3q6pJ27EhtTZzrr5cUtDmeoetKWVayhW/BAcBppmnqmmuu0cyZMx2N44YbblBFRUVKG+tK9aMoBQAAAA8wtX27FIn0twQC0tq1kr1T95JSi1KnTkmHDiVbtkvqdiAmAECSaZpqbLRzvcHhFRUVad26dSltrCvVj6IUAAAAXC4uadOQqXvLl0sTJ0rOFKWukVQjSVq3TjKMgVP4eiXtGOF5AIB8O3/+vPbv3+/4elJJg+OgKNWPohQAAABc7oCk8xq8NmziHH+CpBX2hyRDyWJYZaV0ww2sKwUAbrF582ZJQ4tBThkcx4svvqiLFy86FI27UJQCAACAy5nq7ZWeG3RRu8SsjDWSih2ISZL6p4Uk15XqR1EKAJximqbq6uoUDoedDkWStHLlSpWWlvbdtixLW7ZscTAi96AoBQAAAJcztXu31NWV2rp+veTM1L2k1HWljhyRjh1LtmyVFBnuSQCAPDNN0zW/kpKkkpISrV69OqWNKXwJFKUAAADgYpYkc8h6Ug0N0pQpkrNFqSWSJkuSklcc77+gUqek5x2ICQAK2+XLl7Vnzx5XFaUk1pUaCUUpAAAAuNhhSSeHFKUS5/YhSTfbH1KfgKRENaq6Wlq0SIPWvWLAAQB227Jli+LxuOuLUrt371ZHR4dD0bgHRSkAAAC4mKlYTLq6Zm2fxLn9SkllDsSUEknfvxobWVcKAJxmmqamT5+uhQsXOh1KitWrV6uoqKjvdjQa1bZt2xyMyB0oSgEAAMDFTL34onTpUmprYrpc43BPsFnqulKvvCKdOZNs2SQp7kRQAFCwkutJGYbhdCgpysvLddNNN6W0MYWPohQAAABcbeh6UtdcI82cKTm7nlTSjZLKJQ23rlSbpP32hwQABaqrq0s7duxw3dS9pMFxNaXO+S5IFKUAAADgUsclHR5hPamApLX2hzREkaR1kqQ5c6R585jCBwBO2b59uyKRiGeKUtu3b1d3d7dD0bgDRSkAAAC4lCnLGlzkSRalbpQ0yYGYhpM6hS81Xr4FBwC7mKapqqoqLV261OlQhrVu3bqUaYU9PT3auXOngxE5j6IUAAAAXMrUK69I586ltiaKUm76Fjy1KLV3r9TWlmwxJVkOxAQAhcc0TW3YsEHBYNDpUIZVVVWlZcuWpbQV+rpSFKUAAADgUkPXk6qtlcJhyV1FqZWSSiQlilKWJW3ZkrzvjKTXHIoLAApHb2+vtm7d6tqpe0mD46MoBQAAALjOGUkHNHgN2I0bpcTMh/UOxDSSUkmrJSXWlJo1i3WlAMBue/bsUVdXl+eKUlu2bFE0GnUoGudRlAIAAIALbR52PanGRklaImmaAzGNJjHIMIzh1pWiKAUA+WaapsrLy3XjjTc6HcqoBhelOjs79fzzzzsUjfMoSgEAAMCFTB05Ip04kdrqvvWkklLXldq1S+rsTLZQlAKAfDNNU2vXrlUoFHI6lFFVV1dr0aJFKW2FPIWPohQAAABcaOh6UtOnSwsXSu4sSq2RVCQpUZSKRqVt25L3HZXU4lBcAOB/sVhMmzdvdv3UvSTWlepHUQoAAAAu0y7phSFFqf71pNw46CiXtEKStHixNG2aBq2HVbgDDgDItxdffFHt7e2eLUpt2rRJ8XjcoWicRVEKAAAALrNFkjVsUUpaIGmW/SGlpX9dqQ0bWFcKAOximqaKi4u1atUqp0NJy4YNG1JuX7x4US+99JJD0TiLohQAAABcxtSJE9KhQ6mt7l1PKil1Xalt26SenmQLRSkAyBfTNHXzzTertLTU6VDSUltbq7lz56a0NQ2+3GyBoCgFAAAAlzG1aVNqS1WVtHSp5O6i1DpJhqREUaqnR9q5M3nfa5JOOxQXAPiXZVkyTdMzU/eSWFcqgaIUAAAAXOSKpJ1Dpu6tXy8Fg5K7i1KTJV0vSVq2TJo4cfAUvk3DPQkAkIVXXnlF586d80VRyrIsh6JxDkUpAAAAuMhzkqIjrCc1R1K97RFlJjHICAYThbTU/SjMqRkAkE+maSoYDGrNmjVOh5KRwUWp1tZWvf766w5F4xyKUgAAAHARU+fOSYPXe+1fT8pwIKZMpK4rtWWLFI0mWwpzagYA5JNpmlqxYoUmTpzodCgZmT9/vmbOnJnSVohT+ChKAQAAwEVMbd6c2lJeLi1fLrl76l5SalGqo0N64YVkyz5JFxyICQD8ybIsNTU1eW7qniQZhsG6UqIoBQAAANfokbRNgy9AtHatFApJ3ihKTZd0nSTpppuk0tLBU/g2D/ckAMA4NDc368SJE54sSklSY2Njym2KUgAAAIBjdknqHmE9qWlKFnvcLzE4Ki6W1qwZXJQqvAEHAOSLaZoyDEPr1693OpRxGVxMa2lpUUtLi0PROIOiFAAAAFzCVHv7wOluCd5ZTyopdQrfpk1SPJ5soSgFALlimqYaGho0efJkp0MZl0WLFmnq1KkpbZs2FdaVWilKAQAAwCVMbd06sICT+LXRqlWSN6buJfXH2tgoXbggvfxysmWPpMtOBAUAvmOapmen7klSIBDQhg0bUtoKbQofRSkAAAC4QFTSliFT926+ObEuk7eKUrWS6iUl4g+FNGCdrJik55wJCwB85OTJkzp48KCni1LS0Cl8FKUAAAAA2+2VdHmE9aQqJV1vf0hZSQwyysqklStZVwoAci1ZvBn8SyOvGVyUevXVV3X69GmHorEfRSkAAAC4gKkrV6SdO1NbE+fq6yUFHYgpG6nrSpmmZFnJFopSAJAt0zS1cOFCzZgxw+lQsrJs2TJNnDgxpa2Q1pWiKAUAAAAXMLV9uxSJ9LcEg4mr13lr6l5SalHq9Gnp4MFky3ZJ3U4EBQC+4fX1pJKKioq0bt26lLZCmsJHUQoAAAAOi0syh0zdW75cSnx57MVBxwJJiW/v166VAoGBU/h6lShMAQDG49y5c3rppZd8UZSSCntdKYpSAAAAcNjLki6MsJ5UmaTl9oeUNUPJYlplpXTDDawrBQC5snnzZklSY2Ojw5HkxuCi1L59+3ThwgWHorEXRSkAAAA4zFRvr/TcoIvSJc7R10gqdiCmXOgfLCXXlepHUQoAxss0TYXDYdXV1TkdSk7cdNNNKk1calaSZFmWtmzZ4mBE9qEoBQAAAIeZ2rVL6urqbzEMaf16yZtT95JS15VqbpaOHk22bJUUGeY5AICx+GU9qaSSkhKtXr06pa1QpvBRlAIAAICDLA23nlRDgzRliuTtotRiSVMkJQtsUv8Fla5I2uNATADgbZcuXdLzzz/vq6KUNHQqIkUpAAAAIO8OSTo1wnpSIUk32x9SzgQkbZAkVVdLixczhQ8AsrV161bF43HfFaUG78/u3bvV0dHhUDT2oSgFAAAAB5mKxaSra9b2SZybr5I0wYGYcql/kNHYSFEKALJlmqZqamp0zTXXOB1KTq1evVpFRUV9t2OxmJ4bvNiiD1GUAgAAgINM7d0rXb6c2rphg+TtqXtJqetKvfKKdOZMsmWTpJgTQQGAZyXXkzIMw+lQcqqsrEwrV65MaSuEKXwUpQAAAOCgoetJLVwozZghDbx6nXfdIKlCUrLQNvDXUu2S9tsfEgB41JUrV7Rjxw7fTd1LGrxfTU1NDkViH4pSAAAAcMgxSUdGWE8qIGmt/SHlXJGkdZKk2bOl+fOZwgcA47V9+3ZFIpGCKUpt375d3d3dDkVjD4pSAAAAcMgmWdbgIk2yKLVc0kQHYsqH1Cl8FKUAYHxM01RVVZWWLl3qdCh5sW7dupRpib29vdqxY4eDEeUfRSkAAAA4xNSBA9L586mtiaKUn74FTy1KvfiidPFissWUZDkRFAB4jmma2rBhgwIBf5YyKisrdcMNN6S0+X1dKX++kwAAAPCApiG/kqqrk8JhyV9FqZWSSiUlilKWJW3ZkrzvjKRXHYoLALyjt7dXzz33nG+n7iUN3j+KUgAAAEDOnZH0yghT9yRpvc3x5FOJpNWSpLlzE2tLMYUPADKze/dudXV1qbHRDxfBGNngotTWrVsViUQciib/KEoBAADAAaOtJ7VU0lQHYsqnxCDDMFhXCgDGwzRNlZeX68Ybb3Q6lLzakLxU61WdnZ16/vnnHYom/yhKAQAAwAGmDh+WTpxIbfXfelJJqetK7d4tdXQkW5rEulIAMDrTNLVu3ToVFRU5HUpeVVdXa9GiRSltfp7CR1EKAAAADjCH/EqqpkZauFDyZ1FqtaTEQGrjRikalbZtS953XFKLQ3EBgPvFYjFt3rzZ9+tJJQ2eokhRCgAAAMiZNkl7h526l7gS9oahT/G8ckk3SZIWLZKmTWMKHwCk68UXX9SlS5cKpig1eD83bdqkeDzuUDT5RVEKAAAANtsiyRphPakFkmbZH5ItWFcKAMbDNE2VlJRo5cqVTodii8HrSrW1tWn//v0ORZNfFKUAAABgM1PHj0uHD6e2+nc9qaTUdaW2bZN6epItFKUAYCSmaermm29WaWmp06HYYs6cOZo3b15KW1NTk0PR5BdFKQAAANjM1KZNqS1VVdLSpZLk50t9r5NkSEoUpXp6pB07kve9LumUQ3EBgHtZliXTNAtm6l7S4P3167pSFKUAAABgo05Ju4ZM3duwQQoEJH//UqpK0jJJ0vXXS5MmDZ7Ct2mY5wBAYTtw4IDOnTtHUco0ZVn+u1IrRSkAAADYaJuk6AjrSdVKCtsfkq0Sg4xgUFq/nnWlAGAspmkqGAxqzZo1Todiq8FFqTNnzui1115zKJr8oSgFAAAAGzXp7Fnp5ZdTW/vXkzIciMlO/dMTN26UtmyRotFkiz/XCwGAbJimqRUrVqiiosLpUGw1b948zZqVeuEPP07hoygFAAAAG5navDm1pbxcuvFGyd9T95L6r6i0caPU2Sk9/3yyZb+k804EBQCuVKjrSUmSYRgFsa4URSkAAADYpEfStiFT99aulUIhqTCKUtWSFkmSVqyQJkwYPIVv83BPAoCCdOTIEZ04cUKNjX6+CMbIKEoBAAAAObNTUs8I60lVS7rW/pAckRhkFBdLa9awrhQAjMQ0TRmGoXXr1jkdiiMGF6WOHj2qlpYWh6LJD4pSAAAAsImp9nbphRdSWxNfgBfCelJJ/YOMjRulTZukeDzZQlEKAJJM09T111+vyZMnOx2KIxYvXqxp06altPnt11IUpQAAAGATU1u2DCzASCUl0sqVUmFM3UvqX1eqsVG6eFF66aVkyx5Jl50ICgBcp1DXk0oyDEMbNmxIaaMoBQAAAGQsKmnLkKl7N98slZZKhVWUqpU0V1Ji/0OhgVP44pK2OhQXALjHiRMndOjQoYIuSkn+X1eKohQAAABs8IKkjhHWk6qU1GB7RM5KDDImTJBWrWJdKQAYbNOmTZI05JdChWZwUeq1117TqVOnHIom9yhKAQAAwAamrlyRdu5MbU2ca6+XFHQgJielrivV1CRZVrKFohQANDU16dprr1VNTY3ToThq2bJlmjhxYkpbsmDnBxSlAAAAYANT27ZJ0Wh/SzCYuPqcVIiX+k4tSrW2Sq+/nmzZIanLiaAAwDUKfT2ppGAwqPXr16e0+WkKH0UpAAAA5Flc0qYhU/dWrJAqKqTCWk8qab6kmZKktWulQGDgFL5eJQpTAFCYzp49q5dffpmi1FV+XleKohQAAADy7GVJF0ZYT6pM0nL7Q3KcoeQvxCZNkm68kXWlACBp8+bNkoYWYwrV4OOwb98+XbhwwaFocouiFAAAAPKsSb290nPPpbYmzrHXSgo5EJMbpE7hSy1KNdkeDQC4hWmaCofDqqurczoUV7jppptUmrhUbZ9k4c7rKEoBAAAgz0zt2iV1d/e3GIaUWCKjkL8FTy1KtbQk/kvYqsQ0PgAoPKwnlaq4uFhrEosw9vHLFD6KUgAAAMgjS5I5ZOpeQ4M0ebJU2EWpRZKmSkoW6KT+Cyp1SdrjQEwA4Kz29na98MILamwsxItgjMyv60pRlAIAAEAeHZR0eoT1pIolrbI/JNcISNogSZo2TVqyhHWlAGDr1q2Kx+P8UmqQwcdjz549unz5skPR5A5FKQAAAOSRqWhUGrz0ReIL8FWSJjgQk5v0DzIaGylKAYBpmpoxY4YWLFjgdCiusnr1aoVC/WswxmIxPTd4sUYPoigFAACAPDK1d680+MvcDRukwp66l5S6rtSrr0qtrcmWzZJiTgQFAI5JridlGIbTobhKWVmZVq5cmdLmhyl8FKUAAACQR0PXk7r2WqmmRqIoJUnLJE2UlCzUDVxXql3SPgdiAgBnXLlyRTt37mTq3ggGH5emJu9fqZWiFAAAAPLkqKTmEdaTCkpaa39IrlMkaZ0kadYsacECpvABKFzbt29XJBKhKDWCwcdlx44d6urqciia3KAoBQAAgDzZpHh84C9/EhLn1MuV/IUQUqfwpX7xTVEKQOFoamrS5MmTtWTJEqdDcaW1a9cqEOgv4/T29mrHjh0ORpQ9ilIAAADIE1MHDkjnz6e2JopSfAveL7UotW+fdOFCssWUZDkRFADYzjRNbdiwIaXwgn6VlZW64YYbUtq8vq4U7zQAAADyZOh6UuGwVFcnUZQaaKWkUkmJopRlSVu2JO87K+lVh+ICAPv09vbqueeeY+reGAYfH4pSAAAAwBBnJL0ywnpSkrTe5njcrFjSGklSfb00Zw7rSgEoPLt27VJ3dzdFqTEMPj5bt25VJBJxKJrsUZQCAABAHpiyrMHFlWRRqkHSFAdicrPEIMMwEsco9bh5/+pKADAW0zRVUVGhG2+80elQXG39+tQvda5cuaI9e/Y4FE32KEoBAAAgD0wdPiydPJnaynpSI0ldV2r3bqmjI9nSJNaVAuB3pmlq3bp1KioqcjoUV6uurtbixYtT2rw8hY+iFAAAAPJg6HpSNTXSNddIFKWGs1pSYiC2caMUi0nPPZe874SkZmfCAgAbxGIxbd68mal7afLTulIUpQAAAJBjFyW9qKZBs84aGxPT06QNDsTkdmVKLHguXXedVF3NulIACsfevXt1+fJlilJpamxsTLm9adMmxWIxh6LJDkUpAAAA5NgWSdYI60ldI2mm/SF5wmjrSlGUAuBfpmmqpKREK1eudDoUT9iwIfXLnfb2du3fv9+haLJDUQoAAAA5ZurYMenIkdRW1pMaS+q6Utu3S93dyRaKUgD8yzRNrV69WiUlJU6H4gmzZ8/W/PnzU9qaBv882SMoSgEAACDHTG3alNoyebK0ZIlEUWo06yQZkhJFqZ4eaefO5H0HJZ0c4XkA4F2WZck0TabuZcgv60pRlAIAAEAOdUjaPWTq3oYNUiAgUZQaTaWkGyRJDQ1SZeXgKXybhnkOAHjbgQMHdP78eYpSGRquKGVZ3rtSK0UpAAAA5NA2SdER1pOqk1Rve0TekhhkBIPS+vUatFi8N78FB4DRNDU1qaioSGvWrHE6FE8ZXJQ6e/asXn31VYeiGT+KUgAAAMghU2fOSAcOpLaynlS6+q+otHGjtHWrFIkkWyhKAfAf0zS1YsUKlZeXOx2Kp8ydO1ezZ89OafPiFD6KUgAAAMghU5s3p7aUl0s33ihRlErH+r5/bdwodXZKzz+fbNkv6bwTQQFAXrCe1PgZhuGLdaWKnA5gTJYlnT4tnTsn9fZKxcXStGnSTC4lDMAn6OeyxzEEXKJb0rYhU/fWrZOKiiSKUumolrRY0stavlwqK0usK7VqpaTTks59X+pdTz8HwFtGOFc7fOWKTp48SVFqnDZu3Kgnn3yy73ZTU5Msy5JhGA5GlRl3FqUOH5aeeELatk3asSPxwR1s2jRp1Spp9WrpPe+R5s61P04AGC/6uexxDAEX2impZ4T1pKZLWmh/SJ60UdLLKj4uPTRDavg7SV+TdE6S/jL1ofRzANwqjXO12RUV+qmkNz33XOISrfRhGRlczDt+/LhaWlpUX1/vTEDjYFhpLM9+6dIlVVZWqr29XZMmTcpPJJYl/eIX0re+Jf3qV4oXF6t9wbVqW9KgtsUN6q6uUay4WMHeXpWebVXVy/tU9dI+VR58VYHeXum226Q//3PpjjskD1UFhxO3LLX3RNXWHVFbd0TdsZhicUvBgKHSYFBVpSFVlYZUWVKkgMf3dbBC3fdC3W+pwPbdA/1cNv09uSI9XvzMEzPxDmf4mA8pHntJP3isVYdf3qdDL72ollcP6He/jWrDhjslPeV02O5nWdIvPiF96++kX0nRoiK1L1ykS0uud00/5/pcMYh//r6IOde8FrMn4h3HuVrlSy+q6uBrrjlX8xLLsjR9+nRdbGtT+NpFmr/ket334b9Q3fz5jn820u3v3VGUOn5cuu8+6ZlndGVOnQ7fdbeOvOuPFKmaLFmWjGhUVlFR4kM56Hao7aLm/ud/aN5TP1DZ8aPSrbdKjzwizZmT+zjz7EokqsNtV3Sk7Yoi8cTbYkga+AYNvB0KGJpbVaZ5VWUqC7nzR2/pKtR9L9T9lgpw3z3Sz7l6oOGRYzgSL37miTn/vBavlEbMlqVoNKpgUZEMw1BH+0Utq/0PXTNtgcpC9zkSs2ek9HOzdfiuP3JlP+fqXDGAL/++RMy54LWYPROvx8/VvOhKJKpvPPJ9hW9cpYlVk2VZlqx4XIFgsO8xTn02vFOUeuwx6cMfViRUrH1//YCa77xbhhWXFUz/ABmxqCwjoPqnf6CGv/+yQtGI9PDD0r335jbWPInE4tp39pKa27uGdC5jST6+vnKCGqonKRT01tr1hbrvhbrfUoHuu4f6OdcONDx0DAfz4meemPMfs9filbKNOSpLQdVXlnmr/7aTh/o51+aKqwrv74uY0+W1mD0Vr4f6MD8Y+NmwrLgMI/33167PhvuLUpYl/ff/Ln3xi2pd16hdX31QPVOmSQMqehmLxVR6/qxWPPBXqtnSJH3mM9LnP+/qn/21dvZo16k29cTiWb9WaTCgFTOrVFNekoPI8q9Q971Q91sqwH3PoJ/rinTqdMcRReK9CgWKNaNiriaEhrksbp77OdcNNDyeK7z4mSfm/MfstXilsWNOuw+TR/pvO5ErcsqPf1+ZIOaReS1mz8TrwT7M67ySk91flPrsZ6UvflGH7nm/9n7mf0ixWHaDjKSrr7PsC5/S/B98L7Gdz38++9fNg0MXO7X3zKWcv+6y6ZM0f/LwHzq3KNR9L9T9lgp038fo5461v6ZnDj6u3ad+o9aOoxr8I+yaijqtmPlm3brgvaqtHLA4cB77OdcNNDycK7z4mSfmfvmK2WvxSiPHPO4+zIaYPYVckTN++vvKFjGn8lrMnorXg32Yl3kpJ7u7KPXYY9L73qdDd79Pez/75exfbwR9H+Dvfc91P/nLV0eT5OYTvULd90Ldb6lA932Ufq6146i+s/Pj2ttqKmAEFbdiI75M8v5lNRt1/8qvq6aiLuX+XPdzrhpoeDhXePEzT8xD5Tpmr8UrDR9zTvswN/bfdiJXZB1Lkl/+vnKJmBO8FrOn4vVoH+ZVXsvJ7i1KHTsmLVqk1htu0pZHnszutdKw7r53q+aFXdIrr7hmkbTWzh5tOX4h79tZN2eK634aX6j7Xqj7LRXovo/Sz/360BN6ZM9nFI1HRk0agwWMoIoCId23/Iu6Zf49Kfflsp9zzUDDw7nCi595Yh5ZrmL2WrzS8DHnpQ9zU/9tJ3JFzopSfvn7ygdi9lbMnorXw32YF3kxJ6fb39u7yqRlSR/8oCKhYu366oOJn+TlUyym3V/5R0WKQomrAIxdf8u7SCyuXafabNnW7lNtiuRgDnKuFOq+F+p+SwW676P0c0+/9E19e+ffqDfWnVHikKS4FVNvrFvf3vk3evqlb/bf4cJ+LmsezhVe/MwT8+hyEbPX4pWGjzkvfZhc1H/biVyRM375+8oXYm7LPqA0FFyuoA+zld9zsr1FqV/8QnrmGe376wfUm+1CtekIBtU9tVr7Pvop6ZlnEtt32L6zl9Rr05vcfXVFfrco1H0v1P2WCnTfR+jnfn3oCT2572s52cST+76mXx/6QeKGC/u5rHk4V3jxM0/Mo8tFzF6LVxoac976MLmo/7YTuSJn/PD3lU/E7J2YPRUvfZit/J6T7S1Kfetb6qwNq/nOu2Xle5CRFAyq+c67dWVOnfTQQ/ZscwSdkWjiko02brO5vUtXIlEbtzi8Qt33Qt1vqYD3fZh+rrXjqB7Z85mRn/OopAxz6yN7Pn11EUO5qp/LCY/mCi9+5ok5PdnE7LV4paExj9mHjUNKHyaX9N92Gk+uGAdf5wr54+/LDsRsj4LKFfRhtimEnGxfUerwYelXv9KRO98twxpfBfjimVb940f/VH9223rduWi2/v3Ln03reYYV15E73y398pfSkSPj2nYuHGm7ovFexHLbMz/X5z/wLr1/zVK9Z8VCPfCuP9Dzm54d83nG1e06LZt9P7B7uz717rfq3puX6N3L5unP79ig//u9fx3zeW7Y92z2e6BX9uzQXUtq9dG33TLmY92w31Lu9j0Tju/7CP3cd3Z+XNF4JKebisYj+s7Oj/fddks/lzUP5wov9vFe7Jtz0bdk0qdK2cXsxb5wcMzj7sP+UdIIf0pD+jC5I3fZIh+54ogSx3sQ3+aKq7L5+xp3rpBzfRi5In3kirGNO95c92GZ5Aqf9WHpyFlOltLPFbI3J9tXlHriCcWLi3XkXX8kK1g0rpeI9PZq0pSpuvNDf6H66xan/TwrWKTD//W9ihcXS9///ri2na24ZelI25VxV79f3rVNy9Zu1N/+6/f19R/9UktvXquv/um9OvzyvlGfZ0k63HZFcQfn3Wa77yUTynTHPe/XF7//v/TNnzXpzg/9pZ785tf0zH+O/l46ve/Z7ndS56V2/dMn/kINq9en9Xin91vK3b5nyvF9H6afO9b+mva2mhnP9R5L3Ippb6up4+2vS3JHP5cTHs0VXuzjvdg356JvybRPlcYfsxf7wsEx29aHyfncZRtyRU5k+/c17lwh5/owcoU9MUvkilHRh9mmUHKyfUWpbdvUvuBaRaomj/iQ9gvndd/6ZfrRv/xTX9sre3bqXQ1hvfjcJk2fU6v7/vaLesPb7lJZRWZX64hUTVb7goXStm3j3oVstPdEFYmP/KaOte8f+NQX9LYPflgLGm7QrPp5uuevH9CM8Fzt+t3/G3Pbkbil9h7nfhKf7b7PW9ygDf/l7aq75lpNn1Orxre+Qzesf4MO7N4+5rad3Pds9zvpO5/7hDb8l7fr2htWpL1tt7/nw/mTN63STx/7t5S2j77tFv3nt76R0es4uu/D9HPPHHxcASONKWhxST+T9BVJX5P0W2mss5OAEdSvDj7Wd9vpfi4nPJorvNjHe7FvHi3mfPap443Zi33h4JhH7cP+UdJzg9q+Lel36W1rSB/mcO6yTbq54lUlckLyhwinJH1O0sBu4f9I+tHom/NlrlD2fVhWucKhfpdckX3M5IpU4zrGmZ7v5jpX+KQPS0daOTlfucLGnGxPUcqypB071LakYdSV8iunTNWf/o9/0P98+O91cN9edXV06J8+8RHdfvf7df2aDVnH0La4Qdrxc0kltv/X1v3HGm2Emem+x+NxdXd2qKKyKp2d17Gz9+ns2WJH/jt29oM53ffDL+/Tq8/v0pKVq9Pa97buD8qr7/lvf/RDtR47qnd++K/T2NfU/Xbze55fDr3nVrG04+dD+rndp36T3rcZe5Xokf9Y0h1KJO89oz8lbsW059RvB+x6sp/bMfb23MjDucKLfbwX++bRjnN++9REzJkeZy/2hYOPcdp92DgM6cMktXXndqqz64zQzw17nMOSepUYYEhSi6QySc0DHtMiqX70TfouV1w11mclr7kiD33YeGImV5ArspfhMc72fHcc/NqHpWNwP2drrhhm+/kyvrkRmTp9Wjp3Tm2LG2REo7JCoREfuqLxzbrlrrv1zb/5sOYvXaaSCWV6z0cfyDoEIxpV25Lrpad+IJ3qlWZm/ZIZaeteJENRWcrNvv/k37+t7itXtO6Ot4657Wgkqof/fYn+9XPOnOj9t88t1pvfEVVRlu/7Hzeu0KUL5xWPRfXOP/uobrnrnjG3bSiqtu7FSvyl2ivb9/xk82F9/x++rC99/8cKFmX2p+qF9zxfHHvPT0s6p5R+rivSkbJo4KgmSbpdiUnc0yS1KlGYGuMLutMdLeqKdGpCqHxQP3dKmmlzR5ctD+cKL/bxXuybxzrO+epTpfEdZy/2hQOPcUZ92HD+auyHpPRhKoCi1DD93IjHuVTSDCUGFrOv/n+1pCZJPVf/u6DEQGOqRj3evsoVV7V1R2Ro9KF83nJFnvowiVwxELki/zI+xtme7w4n01zhkz4sHQP7OdtzhfxWlDp3TpLUXV0jK40/7vd+/LP6qz94k5771U/19ad/qVBxSdYhWEVF6p42XZL08iape0HWL5mR1pKaxJzbMVawS2ffN/3f/6X/+fA/6BMPP6rKqdPG3HawqEiTr+67EyZX16TVqY+171964sfq7uzUa3v36Pt//2XNqKvXhv/y9lFf07KKdPr8dO05mdUujEs273ksFtODH/uw3vXnH9OsufMz3rZX3vN8cOo9L31dWqzUfu50R7PS/uZrjlI/K7VKFKXiGuM3rZZOdxzR3MlLU/o5nT/vvSTt4VzhxT7ei31zOsc5H32qNL7j7MW+cOAxzqgPG7cBfZik7lh+vml3jWH6uVGPc1iJAcZaJb7pfrOklyQdldQlaaISg4wx+ShXXNUdi6X16cxLrshjHyaRK5LIFfmX6THO+nx33PzXh6VjYD9ne66QfTnZnk9/b6LyGisuloyxryvQerRFF8+0Kh6P68yJYwpfuyj7GAxDsZJE5/hH7xpzVkzOffrfinXjhuz3ffPP/rf++TMf08ce/FctW7sxrW0bhqFQSfYJeLxCxcUycvC+18ypkySFr12k9vNn9T8f+vsxk5kMQ1ufK9GX/njc4Y9bNu95d2eHDu3fqyMH9uu7X/xbSZIVj8uyLN21pFaffeTJURde9Mp7PpARCMgaNGUrGh3HPGaH3vPlknYrtZ+LxO35tVbfdgb0c+rpsWXbOeXhXOHFPt6LfXM6xzkffWoi5MyPsxf7woHHeMw+bLhdG8dFMwduJ5bhuiqeM0w/N+pxrpf0vBK/TghKqr7a1iypW4mBSJp8kyuuSvezkq9cka8+TCJXDAiaXDHSdhzKFeM63811rvBJH5aOgf2c7blC9uVke4pSxcWSpGBvb2Lu6Sh/dJHeXn3z43+mtXe8VbPnzte3P/MxLVz227S+ARiVZSl49UP7H//pxC+letWV5b5v+umP9c9/+1H91T/8s1a8Ib1Lk0qSZVmKOPgHG+ntlWVZo3a2mb7v8Xhckd40BvyWpbVrerR793ijH79s3vOJk6foH3+SOqf3l08+pn3bNutvvvlvmn41sY/EC+/5YJVTpuri2da+21c6LuvM8XH8FNih97z0dUn/NbWfCwWK03+BE4NuH5c0RWmt/Ne3nQH9nBwsSo6bh3OFF/t4L/bNYx3nfPWpiZAzP85e7AsHHuMx+7BySZcH3O6WdDHDOKWU7QQDdl8U3WbD9HOjHufkWiHb1D+oqJe0WYnjvSb9TfsmV1yVzmcln7kiH31YOjGTK8ZGrshAhsd4XOe7uc4VPunD0jGwn7M9V8i+nGxPUWpaokMqPds65johP3jwq7py+bLu+/QXVVpWrj3mb/Twp/5an/rO45KkIwf2S5K6r3Tq0oXzOnJgv4pCxapdsHDUEIxoVKXnzkiSFm+Q7WtKPX+6Vc3to88hH23fN/3f/6VvPfCX+sCnvqBrrl+ui2cT+1JcWqryiaNfMSRgRPXW3z+jj74zp7uUttc7W9XaM/59/8UTj2razNmaPS8xOnx51zb95N//RW/5o/vG3LZhRDVj6hndOCNnu5O2bN/zuoXXpTy2cspUFZeUDGkfjhfe88GW3rxOv/vf/1M3vfFWlU+cpB9+6+8UCKRx1bpBHHvPr/YpA/u5GRVzpTFXvLiqXdIvJd2kxEKF2yXdls6GjavbSe3nNDWt3+i6i4dzhRf7eC/2zWMd53z1qdL4jrMX+8KBx3jMPmyupBckXavEmha/0zguoTOgD5NUGsx8Xz1lmH5u1OM8QVKNpBclveVqW1jSU0r80qA+3Q37KFdcVRoMjplh85Yr8tSHjRUzuSI95Ir0ZXyMx3O+m+tc4ZM+LB0D+znbc4Xsy8n2FKVmzJCmTVPVy/tkveuPRnzY/u1b9bPHv6vPP/aUyiomSpI+8rVv6aNvu0W/fPIx3f7ue/Wxt9/a9/hDL72oTT/9sapnzdG//Hb01fetoiJVvfRiYgHhmRn8eiFHqkoPyGof+XCPte9bf/4TxaJR/dsXPqV/+8Kn+p73hre9U3/+1QdH3balIs2selnVVfbvtyR1hA7odOv4992Kx/XEP35FZ44fVTBYpJq6sN7zsb/VraN8lpIsFamq9GVJ3nvPb3/3vePettvf8+H8f/f/uc6cOKqv/Ml7VTZxov7rRz4+rm98HHvPZ1jStEhKPzchVK6aijq1drSM/fxlkqKS/k2JLLBaYy5yLkkzKsKaECqXNLCfm+bN+fUezhVe7OO92DePdpzz2acmY870OHuxLxx4jMfsw9Yr8W33D5S4MNOblPG33yl9mKSqUvsX+rXVMP3cmMc5rMSUjPqrt8uUmJrRqURflc5m/ZQrrqoqDclqH/n+vOaKPPRh6cRMrkgPuSJ9GR/j8Zzv5jpX+KQPS8fAfs72XCH7crJhDZ6MOoxLly6psrJS7e3tmjRp9Cr8iH7/93Wx5bh+96Nfju/5OfDGd9ymyeFa6Wc/s33bF7sj+l3LOdu3m/TG8DRNduhEr1D3vVD3WyrgfR+mn3tk96f1y4OP5eUyuQEjqNsX3Kv7Vnypry3bfi6b/r6Qc4UXP/PEnLlMY/ZavNLQmG3vwxzMXbYhV2SfK+SPvy+7EbM9fJ8rfNCHeYXXc3K6/X3GP5wbt9WrVXnwVYXaxjGBNAdCbRdVefA1afVqR7ZfWVKkkEPrJIQChipLnLmig1S4+16o+y0V8L4P08/duuC9eUkckhS3YrptQf83ek73cznh0Vzhxc88MWdmPDF7LV5paMy29mEO5y7bkCtywg9/X3YiZnsURK6gD7NNoeRk+4pS99yjQG+v5v7nf8iIjePKAFkwYlHN++HjCvT2Su95j63bTgoYhuZWlY11BdicMyTNqypTIMMrOuRSoe57oe63VMD7Pkw/V1u5UMtqNipg5HZOdsAIalnNRs2pvEaSO/q5nPBorvDiZ56Y0zfemL0WrzQ0Ztv6MDmfu2xDrsgJP/x92YWY7VEwuYI+zDaFkpPtK0rNmyfddpvmPfUDWYZ9m5Ukywho7tNPSrffLs2da+u2B5pXVZbOcsc5ZUmaW1Vm81aHKtR9L9T9lgp030fo5+5f+XUVBXI7HaUoENL9K7/ed9st/VzWPJwrvPiZJ+b0ZBOz1+KVhsZsSx8md+QuW5ArcsYPf192IGZ7FEyuoA+zVSHkZHvP+P/8z1V2/Kjqn/6BFMvPz86GiMVU//QPVHb8qPRnf2bPNkdQFipSfeUEW7dZXzlBZSHnfwpfqPteqPstFfC+D9PP1VTU6b7lX8zpZu5b/iXVVFy9NLGL+rmc8Giu8OJnnpjTk03MXotXGhpz3vswuaT/thO5Iif88PdlB2K2R0HlCvow2xRCTra3KHXHHdKtt6rh77+s0vNn8z/YiMVUev6sGv7+y9JttyW277CG6kkqDdpz2EuDATVUj38ByVwr1H0v1P2WCnTfR+jnbpl/j97d8ImcbOLuhk/qlvl3J264sJ/LmodzhRc/88Q8ulzE7LV4paEx560Pk4v6bzuRK3LGD39f+UTM3onZU/HSh9nK7znZ3qKUYUiPPKJQNKIVD/yVFMztXMghgkGteOCvFIpFpe9+N7F9h4WCAa2YWWXLtlbMrFLIpo4tHYW674W631KB7vso/dydS/5CH1r5dyoOlmY8FzxgBFUcLNWHVn5D71jykf47XNjPZc3DucKLn3liHl0uYvZavNLwMeelD5OL+m87kStyxi9/X/lCzFXZB5SGgssV9GG28ntOtv8MYM4c6eGHVbOlScu+8Km8bmrZ5x9QzZYm6aGHEtt1iZryEi2bnt/q47Lpk1RTXpLXbYxHoe57oe63VKD7Pko/d8v8e/TgHc+qYfo6SRoziSTvb5i+Tg/e8WzKNxmSe/u5rHk4V3jxM0/Mw8tlzF6LVxo+5pz3YW7rv+1ErsgZv/x95Roxey9mT8VLH2YrP+dkZybv33uvdOiQ5n8xMRdy72e/nPjJXy6+Db/6Oss+/4DmP/mY9NnPJrbnMvMnl0uS9p65lPPXXjZ9Ut/ru1Gh7nuh7rdUoPs+Sj9XU1Gnz77xhzrW/pqeOfi49pz6rU53tEgpyxgamlER1vKZb9JtC+7tuxqGJM/0c1nzcK7w4meemFPlI2avxSsNH3PWfVieY/YUckXO+OXvK1eIuZ/XYvZUvPRhtvJrTjYsyxpzof9Lly6psrJS7e3tmjQpR5Vby5I+9znpC19Q67pG7f7KP6p7anV2g42rc01XPPBXiUrqZz+b2IaLf97X2tmj3afa1B2LZ/1apVd/1ueVbxwLdd8Ldb+lAtz3DPq5rkinTnccUSTeq1CgWDMq5mpCaJjEkOd+Lpv+nlwxlBc/88Sc/5i9Fq80dsxp92HySP9tJ3JFTvnx7ysTxDwyr8XsmXg92Id5nVdycrr9vXNFqaTHHpM+/GFFQsXa99cPqPnOu2VYcVnB9H/EZcSisoyA6p/+gRr+/ssKRSPSww97ppIaicW17+wlNbd3yZAyuhxo8vH1lRPUUD3Jc2syFOq+F+p+SwW67x7q51w70PDQMRzMi595Ys5/zF6LV/JmzJ7ioX7OtbniKi9+VomZmIfjqXg91If5gRc+G94pSknS8ePSffdJzzyjK3PqdOTOd+vwf32vIlWTJcuSEY3KKipKVEYH3Q61XdS8Hz6uuU8/mbg85K23So884sm5plciUR1pu6LDbVcUiSfelsEfsIG3QwFD86rKNLeqzPOXUS7UfS/U/ZYKcN890s+5eqDhkWM4Ei9+5ok5/7wWrzR2zJZlKR6LKlgUck3MnuGRfs7VuWIAP/59Db5NzOPjtZg9E69H+jA/GfzZGJyDJec+G94qSkmJn/394heJxct++UvFi4vVvmCh2hY3qG3J9eqeNl2xkhIFe3pUeu6Mql56UVUv71PlwdcU6O2Vbr9d+rM/S1we0uM/64tbltp7omrrjqitO6LuWEyxuKVgwFBpMKiq0pCqSkOqLClSwOP7Olih7nuh7rdUYPvugX7O9QMNDxzDsXjxM0/MxDuckWJuaT6iLc8+q4/92Z9o8oQSV8XsCR7o51yfKwbx098XMeeW12L2RLwe6MP8KPnZ+Po/PaQJk6v1e295i+OfDe8VpQY6ckT6/velbdukHTukc+eGPmbaNGnVKmn1auk975Hmzs1/XACQKy7t5zw10HDpMQQK3U9+8hP94R/+oU6ePKmZM2c6HY63Dejn2p55RlXR6NDHkCsAuFUa52qxKVMUXL2ac7UcWb16tRYtWqRHH33U6VDS7u/d+RvquXOlz3ym//apU9L581JPj1RSIk2dKnGSA8DL6OeyxzEEXCkcDkuSWlpaKEpla0A/t2jmTH307rv1sfe/n34OgDeMcq72anOz3nDnnfrxz36m1atXOxejz7S0tOj22293OoyMuLMoNdjMmSRcAP5GP5c9jiHgCgOLUgw0cqO7u1unT5/W1KVLpaVLnQ4HAMZnwLlazfz5Oi1yRS4lc0UyD3sFlz4BAABAzlRVVWnSpElqaWlxOhTfOHbsmCR5bqABACMhV+SeV3MFRSkAAADkVDgcZqCRQ8lj6bWBBgCMhlyRW17NFRSlAAAAkFMMNHKrpaVFhmGotrbW6VAAIGfIFbnl1VxBUQoAAAA5xUAjt5KLxhcXFzsdCgDkDLkit7yaKyhKAQAAIKeSAw3LspwOxRdaWlo8Nx0DAMZCrsgtr+YKilIAAADIqXA4rMuXL6utrc3pUHzBqwMNABgNuSK3vJorKEoBAAAgp5InxUzLyA2vDjQAYDTkitzyaq6gKAUAAICcYqCRO7FYTMePH/fkQAMARkOuyB0v5wqKUgAAAMip6dOnq6SkhIFGDpw8eVLRaNSTAw0AGA25Ine8nCsoSgEAACCnAoGA6urqGGjkQPIYenGgAQCjIVfkjpdzBUUpAAAA5ByX+s4NLw80AGAs5Irc8HKuoCgFAACAnGOgkRstLS2aMmWKKioqnA4FAHKOXJEbXs4VFKUAAACQcww0csOrV1MCgHSQK3LDy7mCohQAAAByLhwO6+zZs7py5YrToXialwcaADAWckVueDlXUJQCAABAziVPjo8ePepwJN7m5YEGAIyFXJEbXs4VFKUAAACQc8mT4+bmZmcD8TDLsjw90ACAsZArsuf1XEFRCgAAADk3e/ZsBQIB1grJwtmzZ9XV1eXZgQYAjIVckT2v5wqKUgAAAMi5UCik2bNnM9DIgpcv8Q0A6SBXZM/ruYKiFAAAAPKivr6egUYWkseuvr7e2UAAII/IFdnxeq6gKAUAAIC84FLf2WlpaVF5ebmmTJnidCgAkDfkiux4PVdQlAIAAEBeMNDITnLhWsMwnA4FAPKGXJEdr+cKilIAAADIi3A4rJMnTyoSiTgdiid5+WpKAJAuckV2vJ4rKEoBAAAgL8LhsOLxuI4fP+50KJ7k9YEGAKSDXJEdr+cKilIAAADIi+RJMtMyxsfrAw0ASAe5IjtezxUUpQAAAJAXdXV1khhojMelS5fU1tbm6YEGAKSDXDF+fsgVFKUAAACQFxMmTND06dMZaIxD8ph5eaABAOkgV4yfH3IFRSkAAADkDVdVGh8/DDQAIF3kivHxQ66gKAUAAIC8YaAxPi0tLQqFQpo5c6bToQBA3pErxscPuYKiFAAAAPKGgcb4tLS0qLa2VoEAp+sA/I9cMT5+yBXejRwAAACuFw6HdfToUcXjcadD8RSvX00JADJBrhgfP+QKilIAAADIm3A4rN7eXrW2tjodiqf4YaABAOkiV4yPH3IFRSkAAADkTfJkmWkZmfHDQAMA0kWuGB8/5AqKUgAAAMgbBhqZ6+7u1unTpz0/0ACAdJErMueXXEFRCgAAAHlTVVWlSZMmMdDIwLFjxyR5+xLfAJAJckXm/JIrKEoBAAAgr7iqUmaSx8rrAw0AyAS5IjN+yRUUpQAAAJBXDDQy09LSIsMwVFtb63QoAGAbckVm/JIrKEoBAAAgrxhoZKalpUUzZ85UcXGx06EAgG3IFZnxS66gKAUAAIC8CofDam5ulmVZTofiCc3NzZ6fjgEAmSJXZMYvuYKiFAAAAPIqHA6ro6NDFy9edDoUT/DDJb4BIFPkisz4JVdQlAIAAEBecanvzPhloAEAmSBXZMYvuYKiFAAAAPKKgUb6otGojh8/7ouBBgBkglyRPj/lCopSAAAAyKuamhqVlpYy0EjDyZMnFYvFVF9f73QoAGArckX6/JQrKEoBAAAgrwzDUF1dHQONNCSPkR++/QaATJAr0uenXEFRCgAAAHnHpb7T46eBBgBkilyRHj/lCopSAAAAyDsGGulpaWnR1KlTVV5e7nQoAGA7ckV6/JQrKEoBAAAg7xhopMcvV1MCgPEgV6THT7mCohQAAADyLhwO69y5c+rs7HQ6FFfz00ADADJFrkiPn3IFRSkAAADkXfLk+ejRow5H4m5+GmgAQKbIFenxU66gKAUAAIC8S548My1jZJZl6ejRo74ZaABApsgVY/NbrqAoBQAAgLybPXu2gsEgA41RnD17Vl1dXb4ZaABApsgVY/NbrqAoBQAAgLwrKirS7NmzGWiMwk+X+AaA8SBXjM1vuYKiFAAAAGzBVZVG57eBBgCMB7lidH7LFRSlAAAAYAsGGqNraWlReXm5pkyZ4nQoAOAYcsXo/JYrKEoBAADAFgw0Rpe8mpJhGE6HAgCOIVeMzm+5gqIUAAAAbBEOh3Xy5ElFIhGnQ3ElP13iGwDGi1wxOr/lCopSAAAAsEU4HFY8Htfx48edDsWV/DbQAIDxIFeMzm+5gqIUAAAAbJE8iWZaxvD8NtAAgPEgV4zOb7mCohQAAABsUVdXJ4mBxnAuXbqktrY2Xw00AGA8yBUj82OuoCgFAAAAW0yYMEHTp09noDEMv13iGwDGi1wxMj/mCopSAAAAsE04HFZzc7PTYbhO8pj4aaABAONFrhieH3MFRSkAAADYhkt9D6+lpUWhUEgzZ850OhQAcBy5Ynh+zBUUpQAAAGAbBhrDa2lpUW1trQIBTs8BgFwxPD/mCv/sCQAAAFwvHA7r2LFjisfjTofiKn67mhIAZINcMTw/5gqKUgAAALBNfX29ent7dfr0aadDcZWWlhbV19c7HQYAuAK5Ynh+zBUUpQAAAGCb5De8TMtI5cdvvwFgvMgVw/NjrqAoBQAAANsw0Biqu7tbra2tvhtoAMB4kSuG8muuoCgFAAAA21RWVqqyspKBxgBHjx6V5K9LfANANsgVQ/k1V1CUAgAAgK24qlKq5LHw20ADALJBrkjl11xBUQoAAAC2YqCRqqWlRYZhaM6cOU6HAgCuQa5I5ddcQVEKAAAAtmKgkaqlpUWzZs1ScXGx06EAgGuQK1L5NVdQlAIAAICtkgMNy7KcDsUV/Hg1JQDIFrkilV9zBUUpAAAA2CocDqujo0MXL150OhRX8OtAAwCyQa5I5ddcQVEKAAAAtuJS36n8OtAAgGyQK1L5NVdQlAIAAICtGGj0i0ajOn78uC8HGgCQDXJFPz/nCopSAAAAsNX06dNVWlrKQEPSyZMnFYvFfDnQAIBskCv6+TlXUJQCAACArQzDUF1dHQMN9f8CwI8DDQDIBrmin59zBUUpAAAA2I5LfSf4eaABANkiVyT4OVdQlAIAAIDtGGgktLS0aOrUqSovL3c6FABwHXJFgp9zBUUpAAAA2I6BRoJfr6YEALlArkjwc66gKAUAAADbhcNhnTt3Tp2dnU6H4ig/DzQAIFvkigQ/5wqKUgAAALBd8uT66NGjDkfiLD8PNAAgW+SKBD/nCopSAAAAsF3y5Lq5udnZQBxkWZavBxoAkC1yhf9zBUUpAAAA2G727NkKBoMFvVbImTNn1N3d7duBBgBki1zh/1xBUQoAAAC2Kyoq0uzZswt6oOHnS3wDQC6QK/yfKyhKAQAAwBGFflUlvw80ACAXyBX+zhUUpQAAAOCI+vr6gh9oVFRUaMqUKU6HAgCuRa7wd66gKAUAAABH8O13YuFawzCcDgUAXItc4e9cQVEKAAAAjgiHwzp58qR6e3udDsURfr6aEgDkCrnC37mCohQAAAAcEQ6HZVmWjh8/7nQojvD7QAMAcoFc4e9cQVEKAAAAjkieZBfqtAy/DzQAIBfIFf7OFRSlAAAA4Ii6ujpJhTnQaG9vV3t7u68HGgCQC+QKf+cKilIAAABwRGlpqWpqagpyoOH3S3wDQK6QK/ydKyhKAQAAwDGFelWlQhhoAECukCv8mysoSgEAAMAxhTzQKC4u1owZM5wOBQBcj1zh31xBUQoAAACOKeSBRm1trQIBTscBYCzkCv/mCv/uGQAAAFwvHA7r2LFjisfjTodiK79fTQkAcolc4V8UpQAAAOCYcDis3t5enT592ulQbFUIAw0AyBVyhX9RlAIAAIBjkifbhTYtoxAGGgCQK+QK/6IoBQAAAMcU4kCju7tbra2tvh9oAECukCv8i6IUAAAAHFNZWanKysqCGmgcPXpUkr8v8Q0AuUSu8C+KUgAAAHBUoV1VKbmvfh9oAEAukSv8iaIUAAAAHFWIAw3DMDRnzhynQwEAzyBX+BNFKQAAADiqEAcas2bNUnFxsdOhAIBnkCv8iaIUAAAAHBUOh9Xc3CzLspwOxRbNzc2+n44BALlGrvAnilIAAABwVDgcVmdnpy5cuOB0KLYohEt8A0CukSv8iaIUAAAAHFVol/oulIEGAOQSucKfKEoBAADAUYU00IhGozpx4kRBDDQAIJfIFf5EUQoAAACOmj59ukpLSwtioHHixAnFYjHV19c7HQoAeAq5wp8oSgEAAMBRhmEUzFWVkvtYCN9+A0AukSv8iaIUAAAAHFdoA426ujqHIwEA7yFX+A9FKQAAADiukAYa06ZNU3l5udOhAIDnkCv8h6IUAAAAHFdIA41CmI4BAPlArvAfilIAAABwXDgc1vnz59XZ2el0KHlVSAMNAMg1coX/UJQCAACA4wrlUt+FNNAAgFwjV/gPRSkAAAA4rhAGGpZl6ejRowUz0ACAXCNX+A9FKQAAADhu1qxZCgaDvh5onDlzRt3d3QUz0ACAXCNX+A9FKQAAADiuqKhIc+bM8fVAI7lvhTLQAIBcI1f4D0UpAAAAuILfr6pUaAMNAMgHcoW/UJQCAACAKxTCQKOiokKTJ092OhQA8Cxyhb9QlAIAAIArFMJAIxwOyzAMp0MBAM8iV/gLRSkAAAC4Qjgc1smTJ9Xb2+t0KHlRSJf4BoB8IVf4C0UpAAAAuEI4HJZlWTp+/LjToeRFoQ00ACAfyBX+QlEKAAAArpA8CffrtIxCG2gAQD6QK/yFohQAAABcoa6uTpI/Bxrt7e1qb28vqIEGAOQDucJfKEoBAADAFUpLS1VTU+PLgUahXeIbAPKFXOEvFKUAAADgGuFwWM3NzU6HkXPJfSqkgQYA5Au5wj8oSgEAAMA1/Hqp75aWFhUXF2vGjBlOhwIAnkeu8A+KUgAAAHANPw80amtrFQhw+g0A2SJX+Efh7CkAAABcLxwO69ixY4rH406HklOFdjUlAMgncoV/UJQCAACAa9TX1ysSiejUqVNOh5JTLS0tqq+vdzoMAPAFcoV/UJQCAACAayS/IfbbtIxC/PYbAPKFXOEfFKUAAADgGn4caHR1denMmTMFN9AAgHwhV/gHRSkAAAC4xqRJk1RVVeWrgcbRo0clFdYlvgEgn8gV/kFRCgAAAK7it6sqJfel0AYaAJBP5Ap/oCgFAAAAV/HjQCMQCGjOnDlOhwIAvkGu8AeKUgAAAHAVPw40Zs2apVAo5HQoAOAb5Ap/oCgFAAAAV0kONCzLcjqUnCjEqykBQL6RK/yBohQAAABcJRwOq7OzUxcuXHA6lJwo1IEGAOQTucIfKEoBAADAVfx2qe9CHWgAQD6RK/yBohQAAABcxU8DjWg0qhMnThTkQAMA8olc4Q8UpQAAAOAq1dXVmjBhgi8GGidOnFAsFivIgQYA5BO5wh8oSgEAAMBVDMNQXV2dLwYayX0oxIEGAOQTucIfKEoBAADAdfxyqe/kPtTV1TkcCQD4D7nC+yhKAQAAwHX8NNCYNm2aysvLnQ4FAHyHXOF9FKUAAADgOn4aaBTidAwAsAO5wvsoSgEAAMB1wuGwzp8/r87OTqdDyUohDzQAIN/IFd5HUQoAAACu45dLfRfyQAMA8o1c4X0UpQAAAOA6yZPz5uZmZwPJQjweL+iBBgDkG7nC+yhKAQAAwHVmzZqlYDDo6W+/z5w5o56enoIdaABAvpErvK/I6QAAAACAgeKWpctRS3f+8YdlzJqv505cUCxuKRgwVBoMqqo0pKrSkCpLihQwDKfDlZSIub0nqrbuiNq6I+qOxXTh4hV94uFHVb6gQUfarrguZgDwMnKFPxiWZVljPejSpUuqrKxUe3u7Jk2aZEdcAAAHZNPfkysAZOtKJKrDbVd0pO2KInFLlmXJiscVCAb7HmNISp68hgKG5laVaV5VmcpCznzXOjjmwTFalqWAYbgq5myRKwA4iVzhDen2997cOwAAAPhGJBbXvrOX1NzelXKSbhiGjAGDDA24T5IicUuvX+jUaxc6VV85QQ3VkxQK2rM6xUgxD47RGDDIcDpmAPAycoU/cwVFKQAAADimtbNHu061qScWl5R6ki5JXZFOne44oki8V6FAsWZUzNWEUHnf/cnHN7d36XRHj1bMrFJNeQkxA4CPeLHf9WLMTqAoBQAAAEccutipvWcuDWk/1v6anjn4uHaf+o1aO45q0PfJqqmo04qZb9atC96r2sqFffd0x+LacvyClk2fpPmTy4e8bqHGDABe5sV+14sxO4U1pQAAfVgnBIBdhjthb+04qu/s/Lj2tpoKGEHFrdiIz0/ev6xmo+5f+XXVVNSl3J+PE3cvxpwP5AoAdvFiv+vFmPMh3f7en5MSAQAA4FqtnT1DTth/fegJ/eUv3qB9Z7ZI0qgn7APv33dmi/7yF2/Qrw89kXL/3jOX1NrZU9AxA4CXebHf9WLMTqMoBQAAANtEYnHtOtWW0vb0S9/Ut3f+jXpj3WOerA8Wt2LqjXXr2zv/Rk+/9M2U+3afalPk6loe2fBizADgZV7sd70YsxtQlAIAAIBt9p29pN4BJ9K/PvSEntz3tZy89pP7vqZfH/pB3+3uq1c9ypYXYwYAL/Niv+vFmN2AohQAAABs0RmJqrm9q29Z19aOo3pkz2dyuo1H9nz66uKxCc3tXboSiY779bwYMwB4mRf7XS/G7BYUpQAAAGCLI21XZAy4/Z2dH1c0HsnsRZ6X9OjId0fjEX1n58f7bhtXtzteXowZALzMi/2uF2N2C4pSAAAAyLu4ZelI25W+b5GPtb+mva1mxmtsjL2dmPa2mjre/rqkxMW2D7ddUXzsC04P81reixkAvMyL/a4XY3YTilIAAADIu/aeqCLx/hPnZw4+roARHPrATkl/J8kc0HZU0hckHU5vWwEjqF8dfKzvdiRuqb0n8ykOacf8gqSvSRq8iScl/a/0tpWrmAHAy8gVo/NjrihyOgAAAAD4X1t36jSG3ad+M/y3yOWS/lDSDyXNlzRN0o8lrZI0T4npDWOIWzHtOfVb3Teg7djZC4qWZvZ97Knu1CsbjRjzEkm/kPTq1X9LUoek1yX9kaS28cXc1h3R5NJQRjEDgJeRKzKP2eu5gqIUAAAA8q6tOyJDiekGXZGOlMVah1goaYUS3xzPkhSSdMvV+268+t8YTne0qCvSqQmhckUjET3870/qXz/3yYxi/m+f+6re/I53qygUGj3mkKQGJQZByYHGi5IqJdUrsfBHhjEbGjo4AwC/I1dkFrMfcgXT9wAAAJB33bFY33obpzuaJY2xBsatkuKSXpL0Do3jq1RLpzuOSJKCRUWaPG16pi+gydU1ChYlNjxmzCskHZKUvEL3C5JukFJWvh1Tf8yWEscMAAoJuSId/soVFKUAAACQd7EB621E4r1jP+GCpMtKnHG3jW+bye0YhqFQSUnGzw8VF8swjJTXGtFMSTMk7ZV0UtJZJQYaGRq4nYHHDAAKAbkiPX7KFRSlAAAAkHfBQP/XwKFA8egPjioxHWOJpDdJ+okS625kKLkdy7IU6enJ+PmR3l5ZV69qNGbMkrRciW+9n1diTZPKjDeZsp2BxwwACgG5Ij1+yhWsKQUAAIC8Kw0G+9YJmVExV+q7NYzfSuqRdIekYiUWgf0/ku7JZIvG1e1IAcPQW3//Dn30nWcyivn1zphae6z0YpYSa4U8I2mPpLdntKkhMRtKHDMAKCTkisxi9kOuoCgFAACAvKsqDclqT/x7QqhcNRV1au1oGfrAI5K2SbpXUunVtrdL+hdJOyWtTG97MyrCmhAql5QYGsysmqTqqrKMYu4IXdHp1vaxY04qlbRIiYHRdRltatiYqzx8NSUAGA9yReYxez1XMH0PAAAAeTf4pHnFzDcrYAzz7e5cSZ+VFB7QNlnSA0p7kBEwglo+802jbj8dacc80GUlvgXP8KvfXMUMAF5GrhidH3MFRSkAAADkXWVJkUID1r24dcF7Fbfyc8WguBXTbQvu7bsdChiqLMl8gkBGMXdJOiCpWdKqjDeVs5gBwMvIFaPzY66gKAUAAIC8CxiG5laV9V31urZyoZbVbBz72+SMtxPUspqNmlN5jaTEehvzqsoUMDJfCDajmP9F0v+WdIukac7FDABeRq6wJ2Y3oSgFAAAAW8yrKktZ+vX+lV9XUSC30w6KAiHdv/LrfbctSXMzXB9koLRj/islpo2sy3wbuY4ZALyMXDE8v+YKilIAAACwRVmoSPWVE/pu11TU6b7lX8zpNu5b/iXVVNT13a6vnKCy0PinNngxZgDwMi/2u16M2S0oSgEAAMA2DdWTVBrsPwW9Zf49enfDJ3Ly2nc3fFK3zL+773ZpMKCG6klZv64XYwYAL/Niv+vFmN2AohQAAABsEwoGtGJmVUrbnUv+Qh9a+XcqDpZmvG5IwAiqOFiqD638ht6x5CMp962YWaVQMPvTXS/GDABe5sV+14sxu4E/9gIAAACeUVNeomXTU7/hvWX+PXrwjmfVMD2x0MZYJ+/J+xumr9ODdzyb8g2yJC2bPkk15SUFHTMAeJkX+10vxuw0w7Isa6wHXbp0SZWVlWpvb9ekSf74iRgAYKhs+ntyBYBMHbrYqb1nLg1pP9b+mp45+Lj2nPqtTne0SCnLxxqaURHW8plv0m0L7u27CtFAy6ZP0vzJ5cScJ+QKAHbyYr/rxZhzLd3+nqIUAKAPAw0Admvt7NHuU23qjsWHvb8r0qnTHUcUifcqFCjWjIq5mhAa/oS89OrUiXx/g+zFmHOJXAHAbl7sd70Ycy5RlAIAZIyBBgAnRGJx7Tt7Sc3tXTKU+r3xWJKPr6+coIbqSbatseHFmHOFXAHACV7sd70Yc66k2997//qBAAAA8LRQMKDlM6p03dQKHWm7osNtVxSJJ07dB5/ED7wdChiaV1WmuVVltl8W24sxA4CXebHf9WLMdvP33gEAAMAzykJFWlI9SYumTVR7T1Rt3RG1dUfUHYspFrcUDBgqDQZVVRpSVWlIlSVFChgGMQNAAfFiv+vFmO1CUQoAAACuEjAMTS4NaXJpyOlQ0ubFmAHAy7zY73ox5nzz1qREAAAAAAAA+AJFKQAAAAAAANiOohQAAAAAAABsR1EKAAAAAAAAtqMoBQAAAAAAANtRlAIAAAAAAIDtKEoBAAAAAADAdhSlAAAAAAAAYDuKUgAAAAAAALAdRSkAAAAAAADYjqIUAAAAAAAAbEdRCgAAAAAAALajKAUAAAAAAADbUZQCAAAAAACA7ShKAQAAAAAAwHYUpQAAAAAAAGA7ilIAAAAAAACwHUUpAAAAAAAA2I6iFAAAAAAAAGxHUQoAAAAAAAC2K0rnQZZlSZIuXbqU12AAAM5K9vPJfj8T5AoAKAzkCgDAWNLNFWkVpS5fvixJqq2tzTIsAIAXXL58WZWVlRk/RyJXAEChIFcAAMYyVq4wrDS+4ojH4zp58qQmTpwowzByGiAAwD0sy9Lly5c1a9YsBQKZzfAmVwBAYSBXAADGkm6uSKsoBQAAAAAAAOQSC50DAAAAAADAdhSlAAAAAAAAYDuKUgAAAAAAALAdRSkAAAAAAADYjqIUAAAAAAAAbEdRCgAAAAAAALajKAUAAAAAAADb/f+Xg0bhXu4KnQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here the alternating path after lifting is `x1 - x2 - x3 - x4 - u - u' - v' - w' - w - y1 - y2`. It cannot be `u' - x' - y' - w'` as it is not an alternating path ( the edges `y'w'` and `w'w` are not in the matching )"
      ],
      "metadata": {
        "id": "PgOk4eflz92d"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Finding an augmenting path\n",
        "\n",
        "The following algorithm takes in a graph G and a matching M, and returns an augmenting path on G if found.\n",
        "\n",
        "In each iteration, the algorithm either:\n",
        "1. Finds an augmenting path,\n",
        "2. Finds a blossom and recurses onto the corresponding contracted graph, or\n",
        "3. Concludes there are no augmenting paths.\n",
        "\n",
        "#### Pseudo Code ( [Wikipedia](https://en.wikipedia.org/wiki/Blossom_algorithm) )\n",
        "\n",
        "```\n",
        "function find_augmenting_path(G, M) : P\n",
        "    F ← empty forest\n",
        "    Mark all vertices and edges in G as unmarked and mark all edges of M as marked\n",
        "\n",
        "    // initialization\n",
        "    for each exposed vertex v in G do\n",
        "        Create a singleton tree { v } and add the tree to F\n",
        "    end for\n",
        "\n",
        "    while there is an unmarked vertex v in F with distance(v, root(v)) even do\n",
        "        while there exists an unmarked edge e = { v, w } in G do\n",
        "\n",
        "            // Case 1\n",
        "            if w is not in F then\n",
        "                // w is matched, so add e and w's matched edge to F\n",
        "                x ← vertex matched to w in M\n",
        "                add edges { v, w } and { w, x } to the tree of v\n",
        "            // Case 2\n",
        "            else\n",
        "                // Case 2 - a\n",
        "                if distance(w, root(w)) is odd then\n",
        "                    // Do nothing.\n",
        "                // Case 2 - b\n",
        "                else\n",
        "                    // Case 2 - b - i\n",
        "                    if root(v) ≠ root(w) then\n",
        "                        // Report an augmenting path in F\n",
        "                        P ← path (root(v) → ... → v) → (w → ... → root(w))\n",
        "                        return P\n",
        "                    // Case 2 - b - ii\n",
        "                    else\n",
        "                        // Contract a blossom in G and look for the path in the contracted graph.\n",
        "                        B ← blossom formed by e and edges on the path v → w in T\n",
        "                        G’, M’ ← contract G and M by B\n",
        "                        P’ ← find_augmenting_path(G’, M’)\n",
        "                        P ← lift P’ to G\n",
        "                        return P\n",
        "                    end if\n",
        "                end if\n",
        "            end if\n",
        "            mark edge e\n",
        "        end while\n",
        "        mark vertex v\n",
        "    end while\n",
        "\n",
        "    return empty path\n",
        "end function\n"
      ],
      "metadata": {
        "id": "MK5N2GDulXPh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "When looking at a graph and its matching, and trying to find an augmenting path, remember that you'll only find such a path if the matching isn't already the largest possible. The process involves spotting lonely vertices (exposed vertices) that aren't paired with any other vertex. If there aren't any lonely vertices, it means all vertices are paired up. However, when there's only one lonely vertex, there's only one possibility to start from. To successfully find an augmenting path, you need to have at least two lonely vertices.\n",
        "\n",
        "Now let us use an example with two exposed vertices to understand the working of the algorithm better.\n"
      ],
      "metadata": {
        "id": "XS8d5txgRG1h"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a graph\n",
        "H = nx.Graph()\n",
        "\n",
        "# Add edges\n",
        "edges = [('A', 'B'), ('B', 'C'), ('A', 'G'), ('C', 'D'), ('C', 'F'), ('D', 'E'), ('G', 'H')]\n",
        "H.add_edges_from(edges)\n",
        "\n",
        "# Define the matching\n",
        "M_h = [('B', 'C'), ('D', 'E'), ('G', 'H')]\n",
        "\n",
        "# Layout\n",
        "pos_h = nx.spring_layout(H)\n",
        "\n",
        "nx.draw_networkx(H, pos_h, with_labels=True, node_color='lightblue', node_size=800, font_size=10)\n",
        "nx.draw_networkx_nodes(H, pos_h, nodelist=['A','F'], node_color='red')\n",
        "nx.draw_networkx_edges(H, pos_h, M_h,width=2.5)"
      ],
      "metadata": {
        "id": "_RtRJVQqXOz6",
        "outputId": "dfadbc8a-a452-461c-a775-33da812393af",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.LineCollection at 0x7de51429a8f0>"
            ]
          },
          "metadata": {},
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "Please note that the first three iterations of the algorithm on this graph demonstrates Case 1.\n",
        "\n",
        "Initially, all vertices and edges are unmarked. Then, all matched edges are marked.\n",
        "\n",
        "Starting from an empty forest F:\n",
        "\n",
        "```python\n",
        "for each exposed vertex v:\n",
        "    create a singleton tree { v } and add it to F\n",
        "```\n",
        "\n",
        "In the given example, exposed vertices are A and F. Singleton trees with A and F as roots are constructed and added to F.\n",
        "\n"
      ],
      "metadata": {
        "id": "RgFljGIWUtVN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# code to display singleton trees A and F\n",
        "\n",
        "# Creating an emply forest F\n",
        "F = nx.Graph()\n",
        "\n",
        "# adding singleton sets A and F\n",
        "F.add_nodes_from(['A', 'F'])\n",
        "\n",
        "# Drawing the forest F\n",
        "pos_f = nx.planar_layout(F)\n",
        "pos_f['A'] = (0.5, 0.5)\n",
        "pos_f['F'] = (0.7, 0.5)\n",
        "nx.draw_networkx(F, pos_f, with_labels=True, node_color='lightblue', node_size=800, font_size=10)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "7q0cgwL_cnPe",
        "outputId": "e40e2e65-6976-46db-8db9-dd4deca6d9a5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "The outer while loop iterates on unmarked vertices\n",
        "\n",
        "```python\n",
        "while there is an unmarked vertex v in F with distance(v, root(v)) even do\n",
        "```\n",
        "\n",
        "In the above example, the vertices A and F qualify as v.\n",
        "\n",
        "The next while loop iterates on unmarked edges.\n",
        "```python\n",
        "while there exists an unmarked edge e = { v, w } do\n",
        "```\n",
        "\n",
        "Let's consider A as v and B as w. The edge (A, B) is represented by e.\n",
        "\n",
        "Now, there are two cases:\n",
        "\n",
        "1.   ``` if w is not in F then ```\n",
        "\n",
        "    if w is not in the forest F then it is guaranteed to be matched.\n",
        "\n",
        "    { Why ? A vertex is either matched or exposed (not matched). Therefore, if `w` is not in `F`, i.e aready part of any of the trees, it must be matched to some vertex, because if it was exposed it would have been the root of a tree.}\n",
        "\n",
        "    Let x be matched with w, then add the edges (v,w) and (w,x) to the Tree rooted at v.\n",
        "\n",
        "***In our given example, if `w` is B and it is matched with `C`, then adding edges AB and BC to the tree rooted at A illustrates this process.***\n",
        "\n",
        "2. ``` else ``` i.e w is already in F\n",
        "\n",
        "    a) ``` distance(w, root(w)) is odd then ```\n",
        "\n",
        "      If the distance from `w` to the root of its tree is odd, we don't make any changes. This is because in an alternating tree, the distance between a vertex and its root signifies the level of the vertex in the tree. The odd distance suggests that `w` is in the same level as its root, and altering such a path doesn't yield an augmenting path.\n",
        "  \n",
        "    b) ``` else ``` ie distance of w from its root is even :\n",
        "\n",
        "      Either it belongs to the same tree as v or a different tree.\n",
        "\n",
        "      - ``` if root(v) ≠ root(w) then ```\n",
        "        \n",
        "        it indicates that the edge between `v` and `w` (denoted as `vw`) is a cross edge between different rooted trees. This  implies the presence of an augmenting path.\n",
        "\n",
        "         **RETURNS PATH**\n",
        "\n",
        "         The path starting from root(v) and ending at root(w) is returned as the augmenting path.\n",
        "\n",
        "      - ``` else ``` ie same root\n",
        "    \n",
        "        it suggests that both `v` and `w` belong to the same tree, forming a blossom.\n",
        "\n",
        "        We contract the blossom and recursively call the function on the contracted graph. Then we lift the path returned from the function call and lift it.\n",
        "        This is the required path.\n",
        "\n",
        "\n",
        "  In both cases, the edge `e` is marked.\n",
        "\n",
        "  ***We continue on to the next iteration of the inner loop ( on edges ) and consider the edge AG in this iteration.***\n",
        "\n",
        "  ***G is not in F hence AG and GH are added to the forest. ( Case 1 )***\n",
        "\n",
        "  ***The edge AG is marked.***\n",
        "  \n",
        "Here the while loop on edges ends.\n",
        "\n",
        "In our example the loop exits because no edge from A left.\n",
        "\n",
        "After this, we mark the vertex `v` i.e A in our case.\n",
        "\n",
        "While loop on unmarked vertices continues to the next iteration.\n",
        "\n",
        "The intermediate state of the forest looks like:\n"
      ],
      "metadata": {
        "id": "WqGIoO56clxX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "F.add_edges_from([('A', 'B'), ('B', 'C'), ('A', 'G'), ('G', 'H')])\n",
        "matched_edges = [('B', 'C'), ('G', 'H')]\n",
        "\n",
        "# update positions\n",
        "pos_f['B'] = (0.55, 0.4)\n",
        "pos_f['C'] = (0.55, 0.3)\n",
        "pos_f['G'] = (0.45, 0.4)\n",
        "pos_f['H'] = (0.45, 0.3)\n",
        "nx.draw_networkx(F, pos_f, with_labels=True, node_color='lightblue', node_size=800, font_size=10)\n",
        "nx.draw_networkx_edges(F, pos_f, matched_edges,width=2.5)"
      ],
      "metadata": {
        "id": "D49IH3SjkGSM",
        "outputId": "bf29d2fc-70ce-4900-f90e-a30fa7225bd0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.LineCollection at 0x7de514190160>"
            ]
          },
          "metadata": {},
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The next iteration of the while loop:\n",
        "let us consider the vertex C.\n",
        "\n",
        "C qualifies as v because C is unmarked and at an even distance from A.\n",
        "\n",
        "We enter the while loop that iterates over edges:\n",
        "\n",
        "``` while there exists an unmarked edge e = { v, w } do ```\n",
        "\n",
        "First, let's consider the edge CD. We check if vertex D is present in the forest. Since it is not ( Case 1 ), we add both the edges CD and DE to the forest.\n"
      ],
      "metadata": {
        "id": "rAM6uuAJ81Kz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "F.add_edges_from([('C', 'D'), ('D', 'E')])\n",
        "matched_edges += [('D', 'E')]\n",
        "\n",
        "# update positions\n",
        "pos_f['D'] = (0.5, 0.2)\n",
        "pos_f['E'] = (0.54, 0.1)\n",
        "\n",
        "nx.draw_networkx(F, pos_f, with_labels=True, node_color='lightblue', node_size=800, font_size=10)\n",
        "nx.draw_networkx_edges(F, pos_f, matched_edges,width=2.5)"
      ],
      "metadata": {
        "id": "31A8p8zxrEAn",
        "outputId": "d5f81806-e060-440b-fee6-074e46c57a09",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.LineCollection at 0x7de51414b100>"
            ]
          },
          "metadata": {},
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "In the next iteration, while searching for unmatched edges from vertex C, we consider the edge CF:\n",
        "\n",
        "Since vertex F is already present in the forest F, we proceed to examine the distance of vertex F from its root. In this case, the root of F is F itself, resulting in a distance of 0, which is an even value. Following this, we determine whether vertex F is part of the same tree. Upon discovering that it is not `( Case 2-b-i )`, we identify this situation as the presence of an augmenting path.\n",
        "\n",
        "The augmenting path returned here is `A-B-C-F`. CF being the cross edge.\n"
      ],
      "metadata": {
        "id": "QYNjHW-orC7r"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "F.add_edges_from([('C', 'F')])\n",
        "\n",
        "nx.draw_networkx(F, pos_f, with_labels=True, node_color='lightblue', node_size=800, font_size=10)\n",
        "nx.draw_networkx_edges(F, pos_f, matched_edges,width=2.5)"
      ],
      "metadata": {
        "id": "B3ZqoxMkqwJ2",
        "outputId": "ec044d0c-48f6-4474-bcee-ec8943feb5f5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.LineCollection at 0x7de4f9d28580>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Blossom Contraction Example\n",
        "\n",
        "Consider an intermediate state of the forest as in Figure 1.\n",
        "\n",
        "While exploring edges from H and finds the edge (H,C). We check for a few things :\n",
        "- C is already in F\n",
        "- Distance of C from the root is even.\n",
        "- The root of H and C are the same.\n",
        "\n",
        "Hence, a blossom is detected, as shown in Figure 2.\n"
      ],
      "metadata": {
        "id": "qMkLX08GdX2y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a figure with two subplots\n",
        "fig, axs = plt.subplots(1, 2, figsize=(15, 5))\n",
        "\n",
        "# Creating an emply forest B4\n",
        "F2 = nx.Graph()\n",
        "\n",
        "F2.add_edges_from([('A', 'B'), ('B', 'C'), ('A', 'G'), ('G', 'H')])\n",
        "matched_edges_f2 = [('B', 'C'), ('G', 'H')]\n",
        "\n",
        "pos_F2 = nx.planar_layout(F2)\n",
        "\n",
        "# update positions\n",
        "pos_F2['A'] = (5, 5)\n",
        "pos_F2['B'] = (5.5, 4)\n",
        "pos_F2['C'] = (5.5, 3)\n",
        "pos_F2['G'] = (4.5, 4)\n",
        "pos_F2['H'] = (4.5, 3)\n",
        "\n",
        "plt.subplot(1,2,1)\n",
        "nx.draw_networkx(F2, pos_F2, with_labels=True, node_color='lightblue', node_size=800, font_size=10)\n",
        "nx.draw_networkx_edges(F2, pos_F2, matched_edges_f2,width=2.5)\n",
        "plt.title(\"Figure 1 - F2 Before Adding ('C', 'H')\")\n",
        "\n",
        "# Adding the edge CH to the graph\n",
        "F2.add_edges_from([ ('C', 'H')])\n",
        "\n",
        "plt.subplot(1,2,2)\n",
        "nx.draw_networkx(F2, pos_F2, with_labels=True, node_color='lightblue', node_size=800, font_size=10)\n",
        "nx.draw_networkx_edges(F2, pos_F2, matched_edges_f2,width=2.5)\n",
        "plt.title(\"Figure 2 - F2 After Adding ('C', 'H')\")\n",
        "\n",
        "# Adjust layout\n",
        "plt.tight_layout()\n",
        "\n",
        "# Display the subfigures\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "13qejcLWGe7V",
        "outputId": "889f504b-3daf-498f-adc5-5beb4a51f7d4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 237
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Contracting the blossom and continue searching for augmented paths in the contracted graph.\n",
        "\n",
        "Suppose an augmenting path, P', was found as in Figure 3.\n",
        "\n",
        "We lift the found path P' ( `A-D-E-F` ) into P by expanding the blossom by following the expansion rules. ( Figure 4)"
      ],
      "metadata": {
        "id": "7XnY7dNRfn7S"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create figure and subplots\n",
        "fig, axs = plt.subplots(1, 2, figsize=(15, 5))\n",
        "\n",
        "# Figure 3 - The path P' found in the contracted graph (F3)\n",
        "F3 = nx.Graph()\n",
        "F3.add_edges_from([('A', 'D'), ('D', 'E'), ('E', 'F')])\n",
        "matched_edges_f3 = [('D', 'E')]\n",
        "\n",
        "pos_F3 = nx.planar_layout(F3)\n",
        "pos_F3['A'] = (5, 5)\n",
        "pos_F3['F'] = (7, 5)\n",
        "pos_F3['E'] = (6.5, 4)\n",
        "pos_F3['D'] = (6.5, 3)\n",
        "\n",
        "augmenting_path_f3 = [('A', 'D'), ('D', 'E'), ('E', 'F')]\n",
        "\n",
        "axs[0].set_title(\"Figure 3 - The path P' found in the contracted graph\")\n",
        "nx.draw_networkx_edges(F3, pos_F3, augmenting_path_f3, edge_color='yellow', width=3, ax=axs[0])\n",
        "nx.draw_networkx(F3, pos_F3, with_labels=True, node_color='lightblue', node_size=800, font_size=10, ax=axs[0])\n",
        "nx.draw_networkx_edges(F3, pos_F3, matched_edges_f3, width=2.5, ax=axs[0])\n",
        "nx.draw_networkx_nodes(F3, pos_F3, nodelist=['A'], node_color='green', ax=axs[0])\n",
        "\n",
        "# Figure 4 - The path P after the blossom is expanded (F2)\n",
        "F2.add_edges_from([('A', 'B'), ('B', 'C'), ('A', 'G'), ('G', 'H'), ('C', 'D'), ('D', 'E'), ('E', 'F')])\n",
        "matched_edges_f2 += [('D', 'E')]\n",
        "\n",
        "pos_F2['D'] = (6, 3)\n",
        "pos_F2['E'] = (6, 4)\n",
        "pos_F2['F'] = (6.5, 5)\n",
        "\n",
        "augmenting_path_f2 = [('A', 'B'), ('B', 'C'), ('C', 'D'), ('D', 'E'), ('E', 'F')]\n",
        "\n",
        "axs[1].set_title(\"Figure 4 - The path P after the blossom is expanded\")\n",
        "nx.draw_networkx_edges(F2, pos_F2, augmenting_path_f2, edge_color='yellow', width=3, ax=axs[1])\n",
        "nx.draw_networkx(F2, pos_F2, with_labels=True, node_color='lightblue', node_size=800, font_size=10, ax=axs[1])\n",
        "nx.draw_networkx_edges(F2, pos_F2, matched_edges_f2, width=2.5, ax=axs[1])\n",
        "\n",
        "# Adjust layout\n",
        "plt.tight_layout()\n",
        "\n",
        "# Display the plots\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "Un87Dtktfnni",
        "outputId": "e621906e-4d14-4c73-ba16-cb63b6837667",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 237
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The path P (`A-B-C-D-E-F`) is returned."
      ],
      "metadata": {
        "id": "SfyxOFGJwfZX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Proof of Correctness\n",
        "\n",
        "First we show that given a graph G, and a matching M, if there exists an M-augmenting path in G then one call to the function find_augmenting_path(G,M) will either return an augmenting path or find a blossom.\n",
        "When a blossom is found (`Case 2-b-ii`), it is contracted, and the function is recursively called on the modified graph. If an augmenting path is subsequently found, then this path is lifted to an M-augmented path in G.\n",
        "\n",
        "### Finding an augmenting path or a blossom ( case 2 b )\n",
        "\n",
        "- Let's assume an augmenting path exists say P.\n",
        "\n",
        "- During the initialization, the algorithm chooses both the endpoints of the path P as roots, and hence they will be treated as even.\n",
        "//change vw\n",
        "- Whenever a matched edge `(v,w)` is added to the forest, the first vertex we encounter, `v`, would be labelled as odd and the other endpoint `w`, even.\n",
        "\n",
        "- If P contains k matched edges,  k+2 vertices of P would be labeled as even (one endpoint of each matching edge and the two endpoints of P). Given that P contains 2k+1 vertices in total, the number of even-labeled vertices exceeds odd-labeled vertices.\n",
        "\n",
        "- As a result, there must be two even-labeled vertices adjacent in P. This adjacency can only correspond to the endpoints of an unmatched edge within P.\n",
        "\n",
        "- Thus, there must be an unmatched edge {v, w} along the augmenting path, with v and w both labeled as even.\n",
        "\n",
        "- This edge is examined by the algorithm before termination. If it connects vertices of different trees then the algorithm identifies an augmenting path ( `Case 2-b-i` ). Whereas, if it connects two vertices of the same tree then it identifies a blossom ( `Case 2-b-ii` ).\n",
        "\n",
        "### Lifting an Augmenting Path\n",
        "\n",
        "After identifying an augmenting path or a blossom using the blossom algorithm (Case 2-b), the next step is to lift the augmenting path to an M-augmented path in the original graph G. This process ensures that the matching M can be extended, making progress towards an optimal solution.\n",
        "\n",
        "1. **Lifting an Augmenting Path in Case 2-b-i**\n",
        "\n",
        "   In `Case 2-b-i`, where the algorithm identifies an augmenting path, the lifting process is straightforward. The augmenting path P, which was initially identified within the contracted graph, needs to be lifted to an M-augmented path in the original graph G.\n",
        "\n",
        "   The vertices along this path P alternate between being matched and unmatched. The algorithm then augments the matching M by including the unmatched edges of P while removing the matched edges of P. This augmentation creates a new matching M' that includes the edges from M not in P and the edges from P that were not in M. The cardinality of the matching is increased by one, reflecting the successful augmentation.\n",
        "\n",
        "2. **Lifting a Blossom in Case 2-b-ii**\n",
        "\n",
        "   In `Case 2-b-ii`, where the algorithm identifies a blossom, the lifting process is more intricate due to the contraction of the blossom in the previous step.\n",
        "   \n",
        "   If an augmenting path is found within the contracted blossom, the algorithm needs to backtrack and \"lift\" this path to the original graph G. This involves identifying the specific edges in G that correspond to the contracted edges within the blossom.\n",
        "   \n",
        "   The identified edges are then used to update the matching M in G. This process effectively \"lifts\" the augmenting path from the contracted graph to the original graph.\n",
        "\n",
        "The recursive nature of this process allows the algorithm to handle nested blossoms, ensuring a comprehensive exploration of possible augmentations in the graph.\n",
        "\n",
        "By carefully executing these steps, the blossom algorithm guarantees the correctness of augmenting paths and blossom identification, ultimately contributing to the effectiveness of the overall maximum matching algorithm.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "EFJ-8xsQolXu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## References\n",
        "- https://en.wikipedia.org/wiki/Matching_(graph_theory)\n",
        "\n",
        "- https://en.wikipedia.org/wiki/Blossom_algorithm\n",
        "\n",
        "- https://brilliant.org/wiki/blossom-algorithm/"
      ],
      "metadata": {
        "id": "aXoAYlEem90o"
      }
    }
  ]
}