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;
#define ll long long
#define f(i, x, n) for(int i = x; i < (int)(n); ++i)

int dp[301][301][301], md = 1e9 + 7;
bool bad[301][301][301];

void ad(int &x, int y) { if ((x += y) >= md)x -= md; }

int main(){
	int n, m;
	scanf("%d%d", &n, &m);
	while (m--){
		int l, r, x;
		scanf("%d%d%d", &l, &r, &x);
		f(i, 0, r)f(j, 0, r)if (i == 0 || i != j){
			int z = 1;
			if (i >= l)++z;
			if (j >= l)++z;
			if (x != z)bad[r][i][j] = true;
		}
	}
	dp[1][0][0] = dp[0][1][0] = dp[0][0][1] = 1;
	f(i, 1, n)f(j, 0, i)f(k, 0, i)if (j == 0 || j != k){
		if (bad[i][j][k])continue;
		int &r = dp[i][j][k];
		ad(dp[i + 1][j][k], r);
		ad(dp[i][i + 1][k], r);
		ad(dp[i][j][i + 1], r);
		ad(dp[i + 1][i][k], r);
		ad(dp[j][i + 1][k], r);
		ad(dp[j][i][i + 1], r);
		ad(dp[i + 1][k][i], r);
		ad(dp[j][i + 1][i], r);
		ad(dp[j][k][i + 1], r);
	}
	int an = 0;
	f(i, 0, n)f(j, 0, n)if ((i == 0 || i != j) && !bad[n][i][j])ad(an, dp[n][i][j]), ad(an, dp[i][n][j]), ad(an, dp[i][j][n]);
	printf("%d\n", an);
}