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class Solution {
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 public:
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  bool validSquare(vector<int> &p1, vector<int> &p2, vector<int> &p3, vector<int> &p4) {
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    vector<vector<int>> p{p1, p2, p3, p4};
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    unsigned short ans{0};
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    double scal;
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    vector<double> bar(2);
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    /* compute the barycenter */
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    bar[0] = (p1[0] + p2[0] + p3[0] + p4[0]) / 4.;
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    bar[1] = (p1[1] + p2[1] + p3[1] + p4[1]) / 4.;
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    const double length = pow(p1[0] - bar[0], 2) + pow(p1[1] - bar[1], 2);
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    for (size_t i = 0; i < 4; i++) {
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      if ((pow(p[i][0] - bar[0], 2) + pow(p[i][1] - bar[1], 2)) != length) return false;
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      for (size_t j = i + 1; j < 4; j++) {
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        scal = (bar[0] - p[i][0]) * (bar[0] - p[j][0]) + (bar[1] - p[i][1]) * (bar[1] - p[j][1]);
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        ans += (scal == 0.) ? 1 : 0;
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      }
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    }
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    return ans == 4;
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  }
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};