Problem: Shrimpy Duc is a fat and greedy boy who is always hungry. After a while of searching for food to satisfy his never-ending hunger, Shrimpy Duc finds M&M candies lying unguarded on a L × L grid. There are n M&M candies on the grid, the i-th M&M is currently located at (x_i + 0.5, y_i + 0.5), and has color c_i out of a total of k colors (the size of M&Ms are insignificant).

Shrimpy Duc wants to steal a rectangle of M&Ms, specifically, he wants to select a rectangle with integer coordinates within the grid and steal all candies within the rectangle. Shrimpy Duc doesn't need to steal every single candy, however, he would like to steal at least one candy for each color.

In other words, he wants to select a rectangle whose sides are parallel to the coordinate axes and whose left-bottom vertex (X_1, Y_1) and right-top vertex (X_2, Y_2) are points with integer coordinates satisfying 0 ≤ X_1 < X_2 ≤ L and 0 ≤ Y_1 < Y_2 ≤ L, so that for every color 1 ≤ c ≤ k there is at least one M&M with color c that lies within that rectangle.

How many such rectangles are there? This number may be large, so you only need to find it modulo 10^9 + 7.

Input

The first line contains three positive integers n, k, L (1 ≤ k ≤ n ≤ 2 ⋅ 10^3, 1 ≤ L ≤ 10^9 ) — the number of M&Ms, the number of colors and the length of the grid respectively.

The following n points describe the M&Ms. Each line contains three integers x_i, y_i, c_i (0 ≤ x_i, y_i < L, 1 ≤ c_i ≤ k) — the coordinates and color of the i-th M&M respectively. 

Different M&Ms have different coordinates (x_i ≠ x_j or y_i ≠ y_j for every i ≠ j), and for every 1 ≤ c ≤ k there is at least one M&M with color c.

Output

Output a single integer — the number of rectangles satisfying Shrimpy Duc's conditions, modulo 10^9 + 7.

Examples

Input


4 2 4
3 2 2
3 1 1
1 1 1
1 2 1


Output


20


Input


5 3 10
6 5 3
5 3 1
7 9 1
2 3 2
5 0 2


Output


300


Input


10 4 10
5 4 4
0 0 3
6 0 1
3 9 2
8 7 1
8 1 3
2 1 3
6 3 2
3 5 3
4 3 4


Output


226

Note

Grid for the first sample:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
template <int MOD_>
struct modnum {
  static constexpr int MOD = MOD_;
  static_assert(MOD_ > 0, "MOD must be positive");

 private:
  using ll = long long;
  int v;
  static int minv(int a, int m) {
    a %= m;
    assert(a);
    return a == 1 ? 1 : int(m - ll(minv(m, a)) * ll(m) / a);
  }

 public:
  modnum() : v(0) {}
  modnum(ll v_) : v(int(v_ % MOD)) {
    if (v < 0) v += MOD;
  }
  explicit operator int() const { return v; }
  friend std::ostream& operator<<(std::ostream& out, const modnum& n) {
    return out << int(n);
  }
  friend std::istream& operator>>(std::istream& in, modnum& n) {
    ll v_;
    in >> v_;
    n = modnum(v_);
    return in;
  }
  friend bool operator==(const modnum& a, const modnum& b) {
    return a.v == b.v;
  }
  friend bool operator!=(const modnum& a, const modnum& b) {
    return a.v != b.v;
  }
  modnum inv() const {
    modnum res;
    res.v = minv(v, MOD);
    return res;
  }
  friend modnum inv(const modnum& m) { return m.inv(); }
  modnum neg() const {
    modnum res;
    res.v = v ? MOD - v : 0;
    return res;
  }
  friend modnum neg(const modnum& m) { return m.neg(); }
  modnum operator-() const { return neg(); }
  modnum operator+() const { return modnum(*this); }
  modnum& operator++() {
    v++;
    if (v == MOD) v = 0;
    return *this;
  }
  modnum& operator--() {
    if (v == 0) v = MOD;
    v--;
    return *this;
  }
  modnum& operator+=(const modnum& o) {
    v += o.v;
    if (v >= MOD) v -= MOD;
    return *this;
  }
  modnum& operator-=(const modnum& o) {
    v -= o.v;
    if (v < 0) v += MOD;
    return *this;
  }
  modnum& operator*=(const modnum& o) {
    v = int(ll(v) * ll(o.v) % MOD);
    return *this;
  }
  modnum& operator/=(const modnum& o) { return *this *= o.inv(); }
  friend modnum operator++(modnum& a, int) {
    modnum r = a;
    ++a;
    return r;
  }
  friend modnum operator--(modnum& a, int) {
    modnum r = a;
    --a;
    return r;
  }
  friend modnum operator+(const modnum& a, const modnum& b) {
    return modnum(a) += b;
  }
  friend modnum operator-(const modnum& a, const modnum& b) {
    return modnum(a) -= b;
  }
  friend modnum operator*(const modnum& a, const modnum& b) {
    return modnum(a) *= b;
  }
  friend modnum operator/(const modnum& a, const modnum& b) {
    return modnum(a) /= b;
  }
};
int main() {
  using namespace std;
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  int N, K;
  int L;
  cin >> N >> K >> L;
  using num = modnum<int(1e9) + 7>;
  struct candy {
    array<int, 2> p;
    int c;
  };
  vector<candy> C(N);
  for (int i = 0; i < N; i++) {
    int x, y, c;
    cin >> x >> y >> c;
    c--;
    C[i].p = {x, y};
    C[i].c = c;
  }
  array<vector<num>, 2> weights;
  for (int z = 0; z < 2; z++) {
    sort(C.begin(), C.end(),
         [&](const candy& a, const candy& b) { return a.p[z] < b.p[z]; });
    weights[z].resize(N + 2);
    weights[z][0] = num(-1);
    for (int i = 0; i < N; i++) {
      weights[z][i + 1] = num(C[i].p[z]);
    }
    weights[z][N + 1] = num(L);
    for (int i = 0; i < N; i++) {
      C[i].p[z] = i;
    }
  }
  weights[0].push_back(num(L));
  sort(C.begin(), C.end(),
       [&](const candy& a, const candy& b) { return a.p[1] < b.p[1]; });
  for (int i = 0; i < N; i++) {
    assert(C[i].p[1] == i);
  }
  num ans = 0;
  for (int xlo = 0; xlo < N; xlo++) {
    vector<vector<array<int, 2>>> evts(N + 1);
    vector<vector<array<int, 2>>> pts(
        K, vector<array<int, 2>>({{xlo - 1, -1}, {N, -1}}));
    for (int y = 0; y < N; y++) {
      if (C[y].p[0] < xlo) continue;
      int k = C[y].c;
      evts[y].push_back({N, pts[k].back()[1] + 1});
      while (!pts[k].empty() && pts[k].back()[0] > C[y].p[0]) {
        auto p = pts[k].back();
        pts[k].pop_back();
        evts[y].push_back({p[0], pts[k].back()[1] + 1});
      }
      pts[k].push_back(C[y].p);
    }
    for (int k = 0; k < K; k++) {
      evts[N].push_back({N, pts[k].back()[1] + 1});
      while (pts[k].size() >= 2) {
        auto p = pts[k].back();
        pts[k].pop_back();
        evts[N].push_back({p[0], pts[k].back()[1] + 1});
      }
    }
    set<array<int, 2>> bads;
    bads.insert({xlo, -1});
    bads.insert({N, N + 1});
    auto eval = [&](array<int, 2> l, array<int, 2> r) -> num {
      assert(l[0] >= xlo && r[1] >= l[1]);
      if (l[0] == xlo) return 0;
      return (weights[0][l[0] + 1] - weights[0][xlo + 1]) *
             (weights[1][r[1]] - weights[1][l[1]]);
    };
    num curVal = eval(*bads.begin(), *bads.rbegin());
    for (int yhi = N; yhi > 0; yhi--) {
      evts[yhi].push_back({N, yhi});
      for (auto p : evts[yhi]) {
        auto nt = bads.lower_bound(p);
        if ((*nt)[1] <= p[1]) continue;
        auto pt = nt;
        --pt;
        curVal -= eval(*pt, *nt);
        while ((*pt)[1] > p[1]) {
          auto ppt = pt;
          --ppt;
          curVal -= eval(*ppt, *pt);
          bads.erase(pt);
          pt = ppt;
        }
        curVal += eval(*pt, p);
        curVal += eval(p, *nt);
        bads.insert(nt, p);
      }
      num v = (weights[0][xlo + 1] - weights[0][xlo]) *
              (weights[1][yhi + 1] - weights[1][yhi]) *
              (curVal - eval({N, yhi}, {N, N + 1}));
      ans += v;
    }
  }
  array<num, 2> tot{0, 0};
  for (int z = 0; z < 2; z++) {
    for (int i = 0; i <= N; i++) {
      for (int j = i + 1; j <= N; j++) {
        tot[z] += (weights[z][i + 1] - weights[z][i]) *
                  (weights[z][j + 1] - weights[z][j]);
      }
    }
  }
  ans = tot[0] * tot[1] - ans;
  cout << ans << '\n';
  return 0;
}