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>

static const int
MAXN = 300 + 5;

const int MOD = 1e9 + 7;

template <typename T> inline void mod(T &x) {
  if (x >= MOD) x -= MOD;
  if (x < 0) x += MOD;
}

int N, M;

bool ok[MAXN][MAXN][MAXN];
int dp[MAXN][MAXN][MAXN];

void exec() {
  int i, j, k, l, v, ans(0), r, x;

  scanf("%d%d", &N, &M);

  memset(ok, true, sizeof ok);

  while (M--) {
    scanf("%d%d%d", &l, &r, &x);
    for (i=0; i<r; ++i)
      for (j=0; j<r; ++j)
	if ((l <= i && i <= r) + (l <= j && j <= r) + 1 != x)
	  ok[r][i][j] = ok[r][j][i] = ok[i][r][j] = ok[j][r][i] = ok[i][j][r] = ok[j][i][r] = false;
  }

  for (i=1; i<=N; ++i)
    for (j=0; j<=N; ++j)
      ok[i][i][j] = ok[i][j][i] = ok[j][i][i] = false;
  
  dp[0][0][0] = 1;
  
  for (i=0; i<=N; ++i)
    for (j=0; j<=N; ++j)
      for (k=0; k<=N; ++k)
	if (ok[i][j][k]) {
	  l = std::max(i, std::max(j, k)) + 1;
	  v = dp[i][j][k];
	  if (l <= N) {
	    mod(dp[l][j][k] += v);
	    mod(dp[i][l][k] += v);
	    mod(dp[i][j][l] += v);
	  } else {
	    mod(ans += v);
	  }
	}

  printf("%d\n", ans);
}

int main() {
  if (fopen("E.in", "r") != NULL) {
    freopen("E.in", "r", stdin);
    freopen("E.out", "w", stdout);
  }
  exec();
  return 0;
}