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<cstring>
#include<algorithm>
#define rep(a,b,c) for (int a=b;a<=c;a++)
using namespace std;
const int N=305;
void chkmin(int &x,int y){
	x=min(x,y);
}
void chkmax(int &x,int y){
	x=max(x,y);
}
void add(int &x,int y){
	x=(x+y)%1000000007;
}
int n,m,ans,lmn[4][N],lmx[4][N],f[N][N][N];
int main(){
	scanf("%d%d",&n,&m);
	memset(lmn,127,sizeof(lmn));
	memset(lmx,128,sizeof(lmx));
	rep(i,1,m){
		int x,y,z;
		scanf("%d%d%d",&x,&y,&z);
		chkmin(lmn[z][y],x);
		chkmax(lmx[z][y],x);
	}
	f[1][0][0]=f[0][1][0]=f[0][0][1]=1;
	rep(i,1,n) rep(j,0,i-1) rep(k,0,i-1){
		int fi=i,se=max(j,k),th=min(j,k);
		if ((j==k&&j!=0)||
			se>=lmn[1][i]||
			se< lmx[2][i]||
			th>=lmn[2][i]||
			th< lmx[3][i]){
				f[i][j][k]=
				f[k][i][j]=
				f[j][k][i]=0;
				continue;
			}
		if (i==n){
			add(ans,f[n][j][k]);
			add(ans,f[k][n][j]);
			add(ans,f[j][k][n]);
		}
		for (int l=1;l<=3;l++,swap(i,j),swap(i,k)){
			add(f[fi+1][j][k],f[i][j][k]);
			add(f[i][fi+1][k],f[i][j][k]);
			add(f[i][j][fi+1],f[i][j][k]);
		}
	}
	printf("%d\n",ans);
	return 0;
}