Problem: There are N squares arranged in a row. The squares are numbered 1, 2, ..., N, from left to right.

Snuke is painting each square in red, green or blue. According to his aesthetic sense, the following M conditions must all be satisfied. The i-th condition is:

* There are exactly x_i different colors among squares l_i, l_i + 1, ..., r_i.



In how many ways can the squares be painted to satisfy all the conditions? Find the count modulo 10^9+7.

Constraints

* 1 ≤ N ≤ 300
* 1 ≤ M ≤ 300
* 1 ≤ l_i ≤ r_i ≤ N
* 1 ≤ x_i ≤ 3

Input

Input is given from Standard Input in the following format:


N M
l_1 r_1 x_1
l_2 r_2 x_2
:
l_M r_M x_M


Output

Print the number of ways to paint the squares to satisfy all the conditions, modulo 10^9+7.

Examples

Input

3 1
1 3 3


Output

6


Input

4 2
1 3 1
2 4 2


Output

6


Input

1 3
1 1 1
1 1 2
1 1 3


Output

0


Input

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


Output

108

Solution (in CPP):

Solution:
#include <cstdio>
#include <cstring>
#include <vector>

const int N = 300 + 10, MOD = 1000000007;

int n, f[2][N][N];
std::vector<std::pair<int, int>> pool[N];

void init() {
  int m;
  for (scanf("%d%d", &n, &m); m--;) {
    int l, r, x;
    scanf("%d%d%d", &l, &r, &x);
    pool[r].emplace_back(l, x);
  }
}

int main() {
  init();
  f[0][0][0] = 1;
  for (int i = 1; i <= n; ++i) {
    int c = i & 1;
    memset(f[c], 0, sizeof f[c]);
    for (int j = 0; j < i; ++j) {
      for (int k = 0; k < i; ++k) {
        int cur = f[!c][j][k];
        if (!cur) continue;
        (f[c][j][k] += cur) %= MOD;
        (f[c][i - 1][k] += cur) %= MOD;
        (f[c][j][i - 1] += cur) %= MOD;
      }
    }
    for (auto it : pool[i])
      for (int j = 0; j < i; ++j)
        for (int k = 0; k < i; ++k)
          if ((it.first <= j) + (it.first <= k) + 1 != it.second) f[c][j][k] = 0;
  }
  int ans = 0;
  for (int j = 0; j <= n; ++j)
    for (int k = 0; k <= n; ++k)
      (ans += f[n & 1][j][k]) %= MOD;
  printf("%d\n", ans);
  return 0;
}