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>
#define rg register
#define il inline
using namespace std;
const int mod=1e9+7;
#define _ 310
int n, m, f[_][_][_], cnt[_], ans;
struct Node{int l, x;}c[_][_];
int main(){
	scanf("%d%d", &n, &m);
	int l, r, x;
	for(int i=1; i<=m; ++i){
		scanf("%d%d%d", &l, &r, &x);
		c[r][++cnt[r]]=(Node){l, x};
	}

	f[0][0][0]=1;

	for(int i=0; i<=n; ++i)
		for(int j=0; j<i||!j; ++j)
			for(int k=0; k<j||!k; ++k){
				for(int t=1; t<=cnt[i]; ++t)
					if((j>=c[i][t].l)+(k>=c[i][t].l)!=c[i][t].x-1){
						f[i][j][k]=0;
						break;
					}
				
				if(!f[i][j][k])continue;
				(f[i+1][i][j]+=f[i][j][k])%=mod;
				(f[i+1][j][k]+=f[i][j][k])%=mod;
				(f[i+1][i][k]+=f[i][j][k])%=mod;
			}

	for(int j=0; j<n; ++j)
		for(int k=0; k<j||!k; ++k)
			(ans+=f[n][j][k])%=mod;
	printf("%d", ans);
}