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 <bits/stdc++.h>

using namespace std;

const int mod = 1e9 + 7;

int N, M;
int dp[301][301][301];
vector< pair< int, int > > ween[300];


int main()
{
  cin >> N >> M;

  for(int i = 0; i < M; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    --a, --b;
    ween[b].emplace_back(a, c);
  }

  dp[0][0][0] = 1;

  auto check = [&](int r, int a, int b, int c)
  {
    for(auto &s : ween[r - 1]) {
      int ret = 0;
      ret += a > s.first;
      ret += b > s.first;
      ret += c > s.first;
      if(ret != s.second) return (false);
    }
    return (true);
  };

  for(int i = 0; i < N; i++) {
    for(int j = 0; j < N; j++) {
      for(int k = 0; k < N; k++) {
        int l = max({i, j, k}) + 1;
        if(check(l, l, j, k)) (dp[l][j][k] += dp[i][j][k]) %= mod;
        if(check(l, i, l, k)) (dp[i][l][k] += dp[i][j][k]) %= mod;
        if(check(l, i, j, l)) (dp[i][j][l] += dp[i][j][k]) %= mod;
      }
    }
  }

  int ret = 0;
  for(int i = 0; i <= N; i++) {
    for(int j = 0; j <= N; j++) {
      (ret += dp[i][j][N]) %= mod;
      (ret += dp[i][N][j]) %= mod;
      (ret += dp[N][i][j]) %= mod;
    }
  }

  cout << ret << endl;

}