#include <algorithm>

#include <functional>

  // friend vect operator+(const vect &x, const array<T, D> &y) {
  //   return x + vect(y);
  // }
  // friend vect operator-(const vect &x, const array<T, D> &y) {
  //   return x - vect(y);
  // }
  // friend vect operator+(const vect &x, T a) {
  //   vect r;
  //   for (int d = 0; d < D; ++d)
  //     r.elts[d] = x.elts[d] + a;
  //   return r;
  // }
  // friend vect operator-(const vect &x, T a) {
  //   vect r;
  //   for (int d = 0; d < D; ++d)
  //     r.elts[d] = x.elts[d] - a;
  //   return r;
  // }

  friend bool operator==(const vect &x, const vect &y) {
    return x.elts == y.elts;

  friend vect<bool, D> operator!(const vect &x) {
    vect<bool, D> r;
    for (int d = 0; d < dim; ++d)
      r.elts[d] = !x.elts[d];
    return r;
  }
  friend vect<bool, D> operator&&(const vect &x, const vect &y) {
    vect<bool, D> r;
    for (int d = 0; d < D; ++d)
      r.elts[d] = x.elts[d] && y.elts[d];
    return r;
  }
  friend vect<bool, D> operator||(const vect &x, const vect &y) {
    vect<bool, D> r;
    for (int d = 0; d < D; ++d)
      r.elts[d] = x.elts[d] || y.elts[d];
    return r;
  }
  friend vect<bool, D> operator==(const vect &x, const vect &y) {
    vect<bool, D> r;
    for (int d = 0; d < D; ++d)
      r.elts[d] = x.elts[d] == y.elts[d];
    return r;
  }
  friend vect<bool, D> operator!=(const vect &x, const vect &y) {
    return !(x == y);

  friend bool operator<(const vect &x, const vect &y) {
    return x.elts < y.elts;

  friend vect<bool, D> operator<(const vect &x, const vect &y) {
    vect<bool, D> r;
    for (int d = 0; d < D; ++d)
      r.elts[d] = x.elts[d] < y.elts[d];
    return r;
  }
  friend vect<bool, D> operator>(const vect &x, const vect &y) { return y < x; }
  friend vect<bool, D> operator<=(const vect &x, const vect &y) {
    return !(x > y);
  }
  friend vect<bool, D> operator>=(const vect &x, const vect &y) {
    return !(x < y);
  }
  template <typename U>
  vect<U, D> ifelse(const Loop::vect<U, D> &x,
                    const Loop::vect<U, D> &y) const {
    vect<U, D> r;
    for (int d = 0; d < D; ++d)
      r.elts[d] = elts[d] ? x.elts[d] : y.elts[d];
    return r;

} // namespace Loop
namespace std {

template <typename T, int D> struct equal_to<Loop::vect<T, D> > {
  constexpr bool operator()(const Loop::vect<T, D> &lhs,
                            const Loop::vect<T, D> &rhs) const {
    return equal_to<array<T, D> >()(lhs.elts, rhs.elts);
  }
};
template <typename T, int D> struct less<Loop::vect<T, D> > {
  constexpr bool operator()(const Loop::vect<T, D> &lhs,
                            const Loop::vect<T, D> &rhs) const {
    return less<array<T, D> >(lhs.elts, rhs.elts);
  }
};
template <typename T, int D>
Loop::vect<T, D> max(const Loop::vect<T, D> &x, const Loop::vect<T, D> &y) {
  Loop::vect<T, D> r;
  for (int d = 0; d < D; ++d)
    r.elts[d] = max(x.elts[d], y.elts[d]);
  return r;
}
template <typename T, int D>
Loop::vect<T, D> min(const Loop::vect<T, D> &x, const Loop::vect<T, D> &y) {
  Loop::vect<T, D> r;
  for (int d = 0; d < D; ++d)
    r.elts[d] = min(x.elts[d], y.elts[d]);
  return r;
}
} // namespace std
namespace Loop {