spaceY.ipynb

{
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  {
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     "id": "0d84f6ce-8b21-4055-8db9-bbd6e1f4832c"
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   },
   "source": [
    "# Soft Landing of a Rocket\n",
    "Ian Tsybulkin\n",
    "<img src=\"falcon_lands.jpg\" width=\"300\">\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "0299e985-271b-4252-ba41-9e2e7779c631"
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt \n",
    "import numpy as np\n",
    "\n",
    "# Constats\n",
    "m = 0.05e6          # 0.55e6 full mass\n",
    "\n",
    "G = 9.81            # gravity\n",
    "L = 35.5            # half length\n",
    "D = 1.8             # radius of the rocket\n",
    "F0 = 7.6e6          # full thrust\n",
    "\n",
    "tau = 0.001         # integration step\n",
    "\n",
    "# for more info:  https://en.wikipedia.org/wiki/Falcon_9\n",
    "\n",
    "# Let us assume that we may change the angle of the rocket engines\n",
    "#  at the range of ±6°\n",
    "\n",
    "def lim(u, u_max=0.3):\n",
    "    if u > u_max: return u_max\n",
    "    if u < -u_max: return -u_max\n",
    "    return u"
   ]
  },
  {
   "cell_type": "markdown",
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    "nbpresent": {
     "id": "571a2b89-9b71-45d0-b9f6-e2a2c2d4510f"
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   "source": [
    "Let us assume that just three out of 9 engines are used to control the rocket at a given plane (xz).\n",
    "Thus, our thrust will be splited into two vectors having a little different angles **a** and **(a + u)**\n",
    "\n",
    "\n",
    "$$ I \\frac{d^2a}{dt^2} = -\\frac{3}{9} L F_{th} sin(u) + D F_{th} \\gamma, \\space |\\gamma| < 0.01, \\space I = \\frac{m L^2}{3}$$\n",
    "\n",
    "$$ m \\frac{d^2z}{dt^2} = \\frac{6}{9} F_{th} cos(a) + \\frac{3}{9} F_{th} cos(a+u) - mg  $$\n",
    "\n",
    "$$ m \\frac{d^2x}{dt^2} = -\\frac{6}{9} F_{th} sin(a) - \\frac{3}{9} F_{th} sin(a+u)  $$"
   ]
  },
  {
   "cell_type": "markdown",
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    "nbpresent": {
     "id": "d0ff8530-9f92-4b03-84d3-21b4073146c8"
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   },
   "source": [
    "![black box](black_box.jpeg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "0bcb596a-90bc-4c9e-af01-9b1dbec05b4c"
    }
   },
   "source": [
    "# How to find a rocket thrust ? \n",
    "\n",
    "$$ F_{th} = \\space ?$$\n",
    "\n",
    "\n",
    "Let us assume that the rocket takes off with the full thrust. What will be its velocity and height in 10 seconds?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "6dc5efdd-b328-4620-b9a8-a92e063d094f"
    }
   },
   "outputs": [
    {
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fdgwREZE/5YUXXqBnz5507NiRwYMH59rrPwGY2XJ3jz3RPJ15WEREJBsaOnQoPXv2pHXr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\nREQkbKjYiIiISNhQsREREZGw8f8Ah4XcI/9DPvIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109b1c110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z, dz = 0, 0\n",
    "t = 0\n",
    "\n",
    "Z = [z]\n",
    "DZ = [dz]\n",
    "T = [t]\n",
    "while t < 10:\n",
    "    t += tau\n",
    "    d2z = F0 / m - G\n",
    "    dz += d2z * tau\n",
    "    z += dz * tau\n",
    "    \n",
    "    DZ.append(dz)\n",
    "    Z.append(z)\n",
    "    T.append(t)\n",
    "    \n",
    "fig, (ax1, ax2) = plt.subplots(2, figsize=(9, 12))\n",
    "\n",
    "ax1.plot(T, Z, 'k-')\n",
    "ax1.set(title='Rocket dynamics', ylabel='height')\n",
    "\n",
    "ax2.plot(T, DZ, 'g-')\n",
    "ax2.set(xlabel='time (s)', ylabel='velocity')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "nbpresent": {
     "id": "2404e09d-c633-4290-8b93-cfd65a5bb0e5"
    }
   },
   "source": [
    "$$ z = \\frac{1}{2} \\big(\\frac{F_{th}}{m} - g \\big) (t - t_0)^2  $$\n",
    "\n",
    "$$ \\frac{dz}{dt} = \\big( \\frac{F_{th}}{m} - g \\big) (t - t_0)  $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "ab98e24c-3331-4f57-9872-9f9e4eee3f35"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The time needed to decelerate the rocket from v0 = 50 m/s:\n",
      "t = 9.3 sec\n"
     ]
    }
   ],
   "source": [
    "v0 = 50\n",
    "alpha = 0.1\n",
    "t = v0 / (alpha*F0/m-G)\n",
    "print \"The time needed to decelerate the rocket from v0 = %i m/s:\\nt = %.1f sec\" %(v0, t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "5ac7d60c-5e17-4bf9-8a14-ae0f412cbb59"
    }
   },
   "source": [
    "The rocket accelerating at 45% of its full thrust will reach 340m within 3.4 seconds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "191588b6-6842-45ab-bedc-5b807400ef62"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Height = 231 m\n"
     ]
    }
   ],
   "source": [
    "H = (F0*alpha/m - G)/2*t**2\n",
    "print \"Height = %i m\" % H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "45199fa4-d214-41cb-832b-6d88a05ef5b5"
    }
   },
   "source": [
    "$$ F_{th} = \\bigg( \\frac{\\frac{dz}{dt}^2}{2z} + g \\bigg ) m   $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "9b3d347d-985b-4ad6-b61d-aca6f75a3579"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fth = 760 kN  or 10% of the full thrust\n"
     ]
    }
   ],
   "source": [
    "Fth = (v0**2/2/H+G)*m\n",
    "print \"Fth = %g kN  or %i%% of the full thrust\" % (Fth / 1000., 100*Fth/F0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "5fa8427e-b32b-48a1-8bcf-d9b73f1f23bf"
    }
   },
   "source": [
    "# Fuel consumption\n",
    "The faster the rocket lands the less fuel it consumes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "688497de-cabc-46cf-be50-e753ce5a3a52"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "125 kg/sec at full thrust\n"
     ]
    }
   ],
   "source": [
    "k = m / 400        # fuel consumption at full thrust\n",
    "print \"%i kg/sec at full thrust\" % k\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fuel consumed during landing 115 kg\n"
     ]
    }
   ],
   "source": [
    "fuel = Fth / F0 * t * k\n",
    "print \"Fuel consumed during landing %i kg\" % fuel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "27867593-1be2-43fa-8b1e-87fbb83d23e9"
    }
   },
   "source": [
    "# Finding control"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {
    "collapsed": true,
    "nbpresent": {
     "id": "8cdc2d46-5190-4aee-8758-184fb474c560"
    }
   },
   "outputs": [],
   "source": [
    "def no_control(x,dx,z,dz,a,da,u):\n",
    "    return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "collapsed": true,
    "nbpresent": {
     "id": "acf77d6e-4eba-44d9-bf7a-1f698d0b855d"
    }
   },
   "outputs": [],
   "source": [
    "def init():\n",
    "    # t, x,dx, z,dz, a,da\n",
    "    return 0., 1.5,0.5, H,-v0, 0.,0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "5d96718d-d563-44ca-a66a-78f85129188c"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Landing successful\n",
      "horizontal velocity: 0.025 m/s\n",
      "vertical velocity:   -0.008 m/s\n",
      "angular velocity:    0.00 1/s\n"
     ]
    },
    {
     "data": {
      "image/png": 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MGRw4cIAZM2bQqlUr/vGPf9C2bVtat27N3/72N3bs2OF0qcaYQiruFkon4ANcISLACeB+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\nicgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108d3e2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t, x,dx, z,dz, a,da = init()\n",
    "u = 0\n",
    "\n",
    "Z = [z]\n",
    "dZ = [dz]\n",
    "X = [x]\n",
    "A = [a]\n",
    "U = [u]\n",
    "T = [t]\n",
    "while t < 10:\n",
    "    t += tau\n",
    "    if z < L + 1e-3:\n",
    "        break\n",
    "    \n",
    "    Fth = (dz**2/(z - L-0.99e-3)/2 + G) * m\n",
    "    Fth = min(F0, max(0, Fth))\n",
    "    \n",
    "    u = lqr_control(x,dx,z,dz,a,da,u)\n",
    "    # u = no_control(x,dx,z,dz,a,da,u)\n",
    "    \n",
    "    d2x = - Fth * (6./9. * np.sin(a) + 3./9. * np.sin(a + u)) / m\n",
    "    dx += d2x * tau\n",
    "    x += dx * tau\n",
    "    \n",
    "    d2z = Fth * (6./9. * np.cos(a) + 3./9. * np.cos(a + u)) / m - G\n",
    "    dz += d2z * tau\n",
    "    z += dz * tau\n",
    "    \n",
    "    gama = np.random.uniform(-0.01, 0.01)\n",
    "    d2a = - Fth * ( 3. * L / 3 * np.sin(u)  + 3 * D * gama ) / m / L**2\n",
    "    da += d2a * tau\n",
    "    a += da * tau\n",
    "    \n",
    "    X.append(x)\n",
    "    Z.append(z)\n",
    "    dZ.append(dz)\n",
    "    A.append(a)\n",
    "    U.append(u)\n",
    "    T.append(t)\n",
    "    \n",
    "if abs(x) < 10 and abs(dx) < 0.05 and abs(dz) < 0.2 and abs(a) < 0.1 and abs(da) < 0.05:\n",
    "    print \"Landing successful\"\n",
    "else:\n",
    "    print \"Landing failed\"\n",
    "print \"horizontal velocity: %.3f m/s\" % dx\n",
    "print \"vertical velocity:   %.3f m/s\" % dz\n",
    "print \"angular velocity:    %.2f 1/s\" % da\n",
    "\n",
    "\n",
    "ht = int(len(T) * 0.6)\n",
    "fig, (ax1, ax2, ax3, ax4, ax5) = plt.subplots(5, figsize=(6, 9))\n",
    "\n",
    "ax1.plot(T[ht:], Z[ht:], 'k-')\n",
    "ax1.set(title='Rocket dynamics', ylabel='height')\n",
    "\n",
    "ax2.plot(T[ht:], dZ[ht:], 'k--')\n",
    "ax2.set(ylabel='vertical V')\n",
    "\n",
    "ax3.plot(T[ht:], X[ht:], 'g-')\n",
    "ax3.set(ylabel='x')\n",
    "\n",
    "ax4.plot(T[ht:], A[ht:], 'r-')\n",
    "ax4.set(ylabel='angle')\n",
    "\n",
    "ax5.plot(T[ht:], U[ht:], 'b-')\n",
    "ax5.set(xlabel='time (s)', ylabel='control')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Side view"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cES66KEJiu+20NLhIqdLfhyXu888rQ+L552HBgrhOYrvt4KyzYI89IjDWXDPp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\nbP8A9JUzZicqJPQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a07bbd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, figsize=(6, 8))\n",
    "\n",
    "ax1.plot(X, Z, 'b-')\n",
    "ax1.set(title='Rocket landing', ylabel='height')\n",
    "\n",
    "ax2.plot(X, U, 'r-')\n",
    "ax2.set(xlabel='x', ylabel='control')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"barga1.png\" width=\"300\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LQR\n",
    "Linear-quadrtic regulator\n",
    "\n",
    "https://en.wikipedia.org/wiki/Linear%E2%80%93quadratic_regulator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "2fa2967a-4942-4b0d-99f1-47d95146d95d"
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   "source": [
    "$$ \\frac{d^2z}{dt^2} = \\frac{F_{th}}{m} - g  $$\n",
    "\n",
    "$$ \\frac{d^2x}{dt^2} = -\\frac{F_{th}}{m} a - \\frac{3}{9m} F_{th} u  $$\n",
    "\n",
    "$$ \\frac{d^2a}{dt^2} = -\\frac{2 F_{th}}{3mL} u  $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "a074657c-37a1-446c-b5ce-4d4d9c12a0d4"
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   "source": [
    "Let us decrease the order of the equations by introducing two new variables: \n",
    "\n",
    "$$ v = \\frac{dx}{dt}, \\space w = \\frac{da}{dt} $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "67b61d0d-7b72-4fbb-a7ce-53769fc86d85"
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   "source": [
    "So, we get four linear equation of the first order\n",
    "\n",
    "$$ \\frac{dv}{dt} = -\\frac{F_{th}}{m} a - \\frac{3}{9m} F_{th} u  $$\n",
    "$$ \\frac{dx}{dt} = v  $$\n",
    "$$ \\frac{dw}{dt} = -\\frac{2 F_{th}}{3mL} u  $$\n",
    "$$ \\frac{da}{dt} = w $$\n",
    "\n",
    "\n",
    "or\n",
    "\n",
    "$$ \\frac{\\vec dp}{dt} = A \\vec p + B \\vec u $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "3eb48c2d-fc4f-41ee-adb6-610e01159904"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.        ,   0.        ,   0.        , -16.17420741],\n",
       "       [  1.        ,   0.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   1.        ,   0.        ]])"
      ]
     },
     "execution_count": 270,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fth = (v0**2/(H - L)/2 + G) * m\n",
    "A = np.array([[0, 0, 0, -Fth/m],\n",
    "              [1, 0, 0, 0],\n",
    "              [0, 0, 0, 0],\n",
    "              [0, 0, 1, 0]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "e40b6d65-6bb9-4567-aada-ce1959f9def0"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.39140247],\n",
       "       [ 0.        ],\n",
       "       [-0.30374098],\n",
       "       [ 0.        ]])"
      ]
     },
     "execution_count": 271,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.array([[-3.*Fth/9/m, 0, -2*Fth/3/m/L, 0]]).T\n",
    "B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us introduce a cost function, where Q and R are positive definite matrices:\n",
    "\n",
    "$$ J = \\int_{t_0}^{t_1} (p^T Q p + u^T R u) \\space dt  \\space \\rightarrow min $$\n",
    "\n",
    "$$ U = - K p  $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0.5   0.    0.    0. ]\n",
      " [  0.   10.    0.    0. ]\n",
      " [  0.    0.    1.    0. ]\n",
      " [  0.    0.    0.    1. ]]\n"
     ]
    }
   ],
   "source": [
    "Q = np.eye(4) * np.array([0.5, 10., 1., 1.])\n",
    "R = np.eye(1)\n",
    "print Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"barga.jpg\" width=\"500\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "199477a4-d844-40cd-8e55-9c5be311326b"
    }
   },
   "outputs": [],
   "source": [
    "import scipy.linalg\n",
    "\n",
    "\n",
    "\n",
    "def lqr(A,B,Q,R):\n",
    "    \"\"\"Solve the continuous time lqr controller.    \n",
    "    dx/dt = A x + B u     \n",
    "    cost = integral x.T*Q*x + u.T*R*u\n",
    "    \"\"\"\n",
    "    X = np.matrix(scipy.linalg.solve_continuous_are(A, B, Q, R))\n",
    "     \n",
    "    K = np.matrix(scipy.linalg.inv(R)*(B.T*X))\n",
    "     \n",
    "    eigVals, eigVecs = scipy.linalg.eig(A-B*K)\n",
    "     \n",
    "    return K, eigVals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "565d57b4-02be-400b-ab2d-f62c3e27fa1c"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K: [[   7.90433666    3.16227766 -169.15681547 -158.50185159]] \n",
      "eigen vals: [-3.43004471+2.31477802j -3.43004471-2.31477802j -0.95215402+0.025927j\n",
      " -0.95215402-0.025927j  ]\n"
     ]
    }
   ],
   "source": [
    "K, eigenvals = lqr(A,B,Q,R)\n",
    "print \"K:\",K,\"\\neigen vals:\",eigenvals\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {
    "collapsed": true,
    "nbpresent": {
     "id": "a6f8ea06-f1ca-4a65-9fb8-64d256249df0"
    }
   },
   "outputs": [],
   "source": [
    "def lqr_control(x,dx,z,dz,a,da,u):\n",
    "    K = np.array([ 7.90, 3.16, -169.15, -158.50])\n",
    "    p = np.array([dx,x,da,a])\n",
    "    u = 0.9*u + 0.1*lim(-np.dot(K,p)) # this is for add latency\n",
    "    return u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PID controller\n",
    "\n",
    "https://en.wikipedia.org/wiki/PID_controller\n",
    "\n",
    "<img src=\"pid.png\" width=\"500\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.]])"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R"
   ]
  }
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