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 <algorithm>
#include <cstring>
#include <vector>
using namespace std;

const int MAX_N = 305, MOD = 1000000007;
typedef pair<int, int> pii;

int N, M;
vector<pii> vec[MAX_N];

int f[MAX_N][MAX_N][MAX_N];

inline void update(int &x, int y) {
  x = (x + y) % MOD;
}

int main() {
  scanf("%d%d", &N, &M);
  for (int i = 1, L, R, X; i <= M; ++i) {
    scanf("%d%d%d", &L, &R, &X);
    vec[R].push_back(make_pair(L, X));
  }

  int res = 0;
  
  f[0][0][0] = 1;

  for (int a = 0; a <= N; ++a)
    for (int b = 0; b <= N; ++b)
      for (int c = 0; c <= N; ++c)
	if (f[a][b][c]) {
	  int k = max(a, max(b, c)), &val = f[a][b][c];
	  
	  for (pii x : vec[k]) {
	    int cnt = 0;
	    if (a >= x.first) cnt++;
	    if (b >= x.first) cnt++;
	    if (c >= x.first) cnt++;
	    if (cnt != x.second) val = 0;
	  }
	  
	  if (k < N) {
	    update(f[k + 1][b][c], val);
	    update(f[a][k + 1][c], val);
	    update(f[a][b][k + 1], val);
	  } else {
	    update(res, val);
	  }
	  
	}

  printf("%d\n", res);
  
  return 0;
}