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 mod 1000000007
#define N 309
#define ad(x,y) (x=(x+(y))%mod)
using namespace std;

int n,m,fst[N],pnt[N],len[N],nxt[N],dp[N][N][N]; bool bo[N][N][N];
int main(){
	scanf("%d%d",&n,&m);
	int i,j,k,l,x,y;
	for (i=1; i<=m; i++){
		scanf("%d%d",&x,&y);
		pnt[i]=x; nxt[i]=fst[y]; fst[y]=i;
		scanf("%d",&len[i]);
	}
	for (i=0; i<=n; i++)
		for (j=0; j<=n; j++)
			for (k=0; k<=n; k++){
				x=max(max(i,j),k);
				for (l=fst[x]; l; l=nxt[l]){
					y=pnt[l];
					if ((i>=y)+(j>=y)+(k>=y)!=len[l]) break;
				}
				bo[i][j][k]=(!l);
			}
	dp[0][0][0]=1;
	for (i=0; i<n; i++)
		for (j=0; j<n; j++)
			for (k=0; k<n; k++) if (dp[i][j][k] && bo[i][j][k]){
				x=max(max(i,j),k);
				ad(dp[x+1][j][k],dp[i][j][k]);
				ad(dp[i][x+1][k],dp[i][j][k]);
				ad(dp[i][j][x+1],dp[i][j][k]);
			}
	int ans=0;
	for (i=0; i<=n; i++)
		for (j=0; j<=n; j++)
			for (k=0; k<=n; k++) if (i==n || j==n || k==n)
				if (bo[i][j][k]) ad(ans,dp[i][j][k]);
	printf("%d\n",ans);
	return 0;
}