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>
using namespace std;
typedef long long ll;
const int N=310,p=1e9+7;
int inc(int x,int y){x+=y;return x>=p?x-p:x;}
int mul(int x,int y){return (ll)x*y%p;}
int n,m,dp[N][N][N];
//dp[i][j][k]表示三种颜色最后一次出现位置分别为i,j,k的方案数
//保证i>=j>=k
int L[N][5],R[N][5];
int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i<=n;i++)
	for (int j=1;j<=3;j++)
		L[i][j]=0,R[i][j]=i;
	for (int i=1;i<=m;i++){
		int l,r,x;
		scanf("%d%d%d",&l,&r,&x);
		L[r][x]=max(L[r][x],l);
		R[r][x+1]=min(R[r][x+1],l-1);
	}
	dp[0][0][0]=1;
	for (int i=0;i<n;i++){
		for (int j=0;j<=n;j++)
		for (int k=0;k<=n;k++){
			int v=dp[i][j][k];
			if (!v) continue;
			dp[i+1][j][k]=inc(dp[i+1][j][k],v);
			dp[i+1][i][k]=inc(dp[i+1][i][k],v);
			dp[i+1][i][j]=inc(dp[i+1][i][j],v);
		}
		//剪去不合法状态
		for (int j=0;j<=n;j++)
		for (int k=0;k<=n;k++)
		if (j<L[i+1][2]||j>R[i+1][2]||k<L[i+1][3]||k>R[i+1][3])
			dp[i+1][j][k]=0;
	}
	int ans=0;
	for (int j=0;j<=n;j++)
	for (int k=0;k<=n;k++)
		ans=inc(ans,dp[n][j][k]);
	printf("%d\n",ans);
	return 0;
}