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<vector>
using namespace std;
const int N=330,P=1000000007;
int i,j,k,n,m,l,r,x,L,R,ans;
int f[2][N][N];
vector<int> A[4][N];
bool check(int x,int y,int z) {
	int i,j,k;
	for (i=1;i<=3;i++) {
		for (j=0;j<A[i][x].size();j++) {
			k=0;
			if (A[i][x][j]<=z) k++;
			if (A[i][x][j]<=y) k++;
			if (A[i][x][j]<=x) k++;
			if (k!=i) return 0;
		}
	}
	return 1;
}
int main() {
	scanf("%d%d",&n,&m);
	for (i=1;i<=m;i++) {
		scanf("%d%d%d",&l,&r,&x);
		A[x][r].push_back(l);
	}
	L=0;R=1;f[R][0][0]=1;
	for (i=1;i<n;i++) {
		L^=1;R^=1;
		for (j=0;j<i;j++)
			for (k=0;k<=j;k++) if (f[L][j][k]) {
				int t=f[L][j][k];
				f[L][j][k]=0;
				if (!check(i,j,k)) continue;
				f[R][j][k]=(f[R][j][k]+t)%P;
				f[R][i][k]=(f[R][i][k]+t)%P;
				f[R][i][j]=(f[R][i][j]+t)%P;
			}
	}
	for (j=0;j<n;j++)
		for (k=0;k<=j;k++) if (f[R][j][k] && check(n,j,k)) ans=(3ll*f[R][j][k]+ans)%P;
	printf("%d\n",ans);
}