{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experimental API: Non-factorizing background\n",
    "\n",
    "This is an advanced tutorial, you should check out the basic tutorial first. Here, we consider a case where the background is non-factorizing and how to still handle this case with COWs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm, expon\n",
    "import numpy as np\n",
    "from iminuit.cost import ExtendedUnbinnedNLL\n",
    "from iminuit import Minuit\n",
    "\n",
    "from sweights.testing import make_classic_toy\n",
    "from sweights.util import plot_binned, make_bernstein_pdf\n",
    "from sweights.independence import kendall_tau\n",
    "from sweights.experimental import Cows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first generate a toy distribution. The background in the m-variable is an exponential whose slope depends on the t-variable, thus breaking factorization between m and t."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mrange = (0.0, 1.0)\n",
    "trange = (0.0, 0.5)\n",
    "tsplit = 0.2\n",
    "\n",
    "toy = make_classic_toy(\n",
    "    1, s=4000, b=10000, mrange=mrange, trange=trange, mb_mu=lambda t: 0.1 + 10 * (t / 1.5)\n",
    ")\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "plt.sca(ax[0])\n",
    "plot_binned(toy[0], bins=100, color=\"k\", label=\"total\")\n",
    "plot_binned(toy[0][toy[2]], bins=100, marker=\".\", color=\"C0\", label=\"signal\")\n",
    "plt.sca(ax[1])\n",
    "plot_binned(toy[1], bins=100, color=\"k\", label=\"total\")\n",
    "plot_binned(toy[1][toy[2]], bins=100, marker=\".\", color=\"C0\", label=\"signal\")\n",
    "plt.axvline(tsplit, ls=\"--\", color=\"0.5\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can see the factorization violation by eye if the normalized pure background is plotted in intervals of the t-variable. The slopes are different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tsplit = np.quantile(toy[1], (0, 0.3, 0.6, 1.0))\n",
    "for ta, tb in zip(tsplit[:-1], tsplit[1:]):\n",
    "    m = toy[0][~toy[2]]\n",
    "    t = toy[1][~toy[2]]\n",
    "    ma = (ta <= t) & (t < tb)\n",
    "    plot_binned(m[ma], density=True)\n",
    "plt.semilogy()\n",
    "plt.xlabel(\"m\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As explained in the notebook about factorization tests, one can use Kendall's tau test to detect the non-factorization if a pure background-only sample is available. We can get a background-only sample from the side bands. The p-value is indeed tiny."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(4.619421569260017e-68)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ma = (toy[0] < 0.2) | (toy[0] > 0.8)\n",
    "val, err, pvalue = kendall_tau(toy[0][ma], toy[1][ma])\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's ignore the factorization violation and fit the m-distribution to obtain pdfs for signal and background. We model the background with a sum of Bernstein basis polynomials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -2.413e+05 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 249 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.16e-06 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.4 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> s </td>\n",
       "        <td> 3.96e3 </td>\n",
       "        <td> 0.22e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> b1 </td>\n",
       "        <td> 6.33e3 </td>\n",
       "        <td> 0.14e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> b2 </td>\n",
       "        <td> 2.0e3 </td>\n",
       "        <td> 0.4e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> b3 </td>\n",
       "        <td> 1.63e3 </td>\n",
       "        <td> 0.10e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> mu </td>\n",
       "        <td> 0.5006 </td>\n",
       "        <td> 0.0029 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 1 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 0.100 </td>\n",
       "        <td> 0.004 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
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       "        <td></td>\n",
       "        <th> s </th>\n",
       "        <th> b1 </th>\n",
       "        <th> b2 </th>\n",
       "        <th> b3 </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s </th>\n",
       "        <td> 4.78e+04 </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.011e6 <strong>(0.371)</strong> </td>\n",
       "        <td style=\"background-color:rgb(137,137,250);color:black\"> -0.07e6 <strong>(-0.867)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,164,164);color:black\"> 12e3 <strong>(0.573)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.598e-3 </td>\n",
       "        <td style=\"background-color:rgb(250,131,131);color:black\"> 678.308e-3 <strong>(0.793)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b1 </th>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.011e6 <strong>(0.371)</strong> </td>\n",
       "        <td> 1.9e+04 </td>\n",
       "        <td style=\"background-color:rgb(170,170,250);color:black\"> -0.030e6 <strong>(-0.616)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 6e3 <strong>(0.466)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,216,216);color:black\"> 88.514e-3 <strong>(0.223)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 146.275e-3 <strong>(0.271)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b2 </th>\n",
       "        <td style=\"background-color:rgb(137,137,250);color:black\"> -0.07e6 <strong>(-0.867)</strong> </td>\n",
       "        <td style=\"background-color:rgb(170,170,250);color:black\"> -0.030e6 <strong>(-0.616)</strong> </td>\n",
       "        <td> 1.26e+05 </td>\n",
       "        <td style=\"background-color:rgb(151,151,250);color:black\"> -27e3 <strong>(-0.763)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -73.260e-3 <strong>(-0.072)</strong> </td>\n",
       "        <td style=\"background-color:rgb(157,157,250);color:black\"> -988.473e-3 <strong>(-0.712)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b3 </th>\n",
       "        <td style=\"background-color:rgb(250,164,164);color:black\"> 12e3 <strong>(0.573)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 6e3 <strong>(0.466)</strong> </td>\n",
       "        <td style=\"background-color:rgb(151,151,250);color:black\"> -27e3 <strong>(-0.763)</strong> </td>\n",
       "        <td> 9.63e+03 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -13.657e-3 <strong>(-0.048)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,186,186);color:black\"> 163.929e-3 <strong>(0.427)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.598e-3 </td>\n",
       "        <td style=\"background-color:rgb(250,216,216);color:black\"> 88.514e-3 <strong>(0.223)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -73.260e-3 <strong>(-0.072)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -13.657e-3 <strong>(-0.048)</strong> </td>\n",
       "        <td> 8.24e-06 </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0e-6 <strong>(-0.021)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,131,131);color:black\"> 678.308e-3 <strong>(0.793)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 146.275e-3 <strong>(0.271)</strong> </td>\n",
       "        <td style=\"background-color:rgb(157,157,250);color:black\"> -988.473e-3 <strong>(-0.712)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,186,186);color:black\"> 163.929e-3 <strong>(0.427)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0e-6 <strong>(-0.021)</strong> </td>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -2.413e+05                 │              Nfcn = 249              │\n",
       "│ EDM = 1.16e-06 (Goal: 0.0002)    │            time = 0.4 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name  │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ s     │  3.96e3   │  0.22e3   │            │            │    0    │         │       │\n",
       "│ 1 │ b1    │  6.33e3   │  0.14e3   │            │            │    0    │         │       │\n",
       "│ 2 │ b2    │   2.0e3   │   0.4e3   │            │            │    0    │         │       │\n",
       "│ 3 │ b3    │  1.63e3   │  0.10e3   │            │            │    0    │         │       │\n",
       "│ 4 │ mu    │  0.5006   │  0.0029   │            │            │    0    │    1    │       │\n",
       "│ 5 │ sigma │   0.100   │   0.004   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬─────────────────────────────────────────────────────────────────────────┐\n",
       "│       │           s          b1          b2          b3          mu       sigma │\n",
       "├───────┼─────────────────────────────────────────────────────────────────────────┤\n",
       "│     s │    4.78e+04     0.011e6     -0.07e6        12e3   -1.598e-3  678.308e-3 │\n",
       "│    b1 │     0.011e6     1.9e+04    -0.030e6         6e3   88.514e-3  146.275e-3 │\n",
       "│    b2 │     -0.07e6    -0.030e6    1.26e+05       -27e3  -73.260e-3 -988.473e-3 │\n",
       "│    b3 │        12e3         6e3       -27e3    9.63e+03  -13.657e-3  163.929e-3 │\n",
       "│    mu │   -1.598e-3   88.514e-3  -73.260e-3  -13.657e-3    8.24e-06       -0e-6 │\n",
       "│ sigma │  678.308e-3  146.275e-3 -988.473e-3  163.929e-3       -0e-6    1.53e-05 │\n",
       "└───────┴─────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bern = make_bernstein_pdf(2, *mrange)\n",
    "\n",
    "# m-density for fitting and plotting (not normalized)\n",
    "def m_density(x, s, b1, b2, b3, mu, sigma):\n",
    "    ds = norm(mu, sigma)\n",
    "    snorm = np.diff(ds.cdf(mrange))\n",
    "    return s / snorm * ds.pdf(x) + b1 * bern[0](x) + b2 * bern[1](x) + b3 * bern[2](x)\n",
    "\n",
    "\n",
    "# m-model for an extended maximum-likelihood fit, must return...\n",
    "# - integral as first argument\n",
    "# - density as second argument\n",
    "# see iminuit documentation for more information\n",
    "def m_model(x, s, b1, b2, b3, mu, sigma):\n",
    "    return (s + b1 + b2 + b3, m_density(x, s, b1, b2, b3, mu, sigma))\n",
    "\n",
    "\n",
    "mi = Minuit(\n",
    "    ExtendedUnbinnedNLL(toy[0], m_model),\n",
    "    s=10000,\n",
    "    mu=0.5,\n",
    "    sigma=0.1,\n",
    "    b1=10000,\n",
    "    b2=10000,\n",
    "    b3=10000\n",
    ")\n",
    "mi.limits[\"s\", \"b1\", \"b2\", \"b3\"] = (0, None)\n",
    "mi.limits[\"mu\"] = mrange\n",
    "mi.limits[\"sigma\"] = (0, None)\n",
    "\n",
    "mi.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We construct the pdfs for signal and background."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def spdf(m):\n",
    "    return m_density(m, 1, 0, 0, 0, *mi.values[-2:])\n",
    "\n",
    "\n",
    "def bpdf(m):\n",
    "    b1, b2, b3 = mi.values[1:4]\n",
    "    bt = b1 + b2 + b3\n",
    "    return m_density(m, 0, b1/bt, b2/bt, b3/bt, *mi.values[-2:])\n",
    "\n",
    "mp = np.linspace(*mrange, 1000)\n",
    "plt.plot(mp, spdf(mp))\n",
    "plt.plot(mp, bpdf(mp));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We construct classic sWeights, COWs with a single background component, and finally COWs with multiple background components. For the last case, we use the Bernstein basis polynomials as background components. As explained in the paper, using multiple background components increases the variance of the weights and reduces the statistical precision of any derived results, but has the potential to avoid the bias from non-factorization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute classic sWeights\n",
    "sweight = Cows(toy[0], spdf, bpdf, range=mrange)\n",
    "# compute COWs with integration method, flat norm, and same two components\n",
    "cow = Cows(None, spdf, bpdf, range=mrange)\n",
    "# compute classic sWeights with several background components\n",
    "# nf stands for non-factorizing\n",
    "sweight_nf = Cows(toy[0], spdf, bern, range=mrange)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the weighted distributions. Only the sWeights computed with multiple background components recover the exponential distribution of the projected signal in the t-variable. The other projections are not exponential."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for method, weighter in (\n",
    "    (\"sWeights\", sweight),\n",
    "    (\"COWs\", cow),\n",
    "    (\"sWeights NF\", sweight_nf),\n",
    "):\n",
    "    plot_binned(toy[1], weights=weighter(toy[0]), label=method)\n",
    "plt.semilogy()\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also see this with an extended binned fit, which provides us with a chi2 gof test statistic. Only the COWs analysis with multiple background components reproduces the true slope of 0.2 within uncertainties and yields a good fit (chi2/ndof around 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sWeights  : slope = 0.23 +/- 0.01 (chi2/ndof = 5.9)\n",
      "COWs      : slope = 0.23 +/- 0.01 (chi2/ndof = 8.8)\n",
      "sWeights NF: slope = 0.20 +/- 0.01 (chi2/ndof = 0.4)\n"
     ]
    }
   ],
   "source": [
    "from iminuit.cost import ExtendedBinnedNLL\n",
    "\n",
    "for method, weighter in ((\"sWeights\", sweight), (\"COWs\", cow), (\"sWeights NF\", sweight_nf)):\n",
    "    # get signal weights\n",
    "    w = weighter(toy[0])\n",
    "\n",
    "    # do the minimisation\n",
    "\n",
    "    val, xe = np.histogram(toy[1], weights=w)\n",
    "    var = np.histogram(toy[1], bins=xe, weights=w**2)[0]\n",
    "\n",
    "    data = np.transpose((val, var))\n",
    "    cost = ExtendedBinnedNLL(data, xe, lambda x, n, slope: n * expon.cdf(x, 0, slope))\n",
    "    tmi = Minuit(cost, n=10000, slope=0.1)\n",
    "    tmi.limits[\"n\", \"slope\"] = (0.01, None)\n",
    "    tmi.migrad()\n",
    "    tmi.hesse()\n",
    "    val = tmi.values[\"slope\"]\n",
    "    err = tmi.errors[\"slope\"]\n",
    "    print(f\"{method:10}: slope = {val:.2f} +/- {err:.2f} \"\n",
    "          f\"(chi2/ndof = {tmi.fmin.reduced_chi2:.1f})\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}