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>
using namespace std;
const int P=1e9+7;
const int N=305;
#define fi first
#define se second
int n,m,f[N][N][N];
vector<pair<int,int> >a[N];
bool check(int i,int j,int k){
	int si=a[i].size();
	for(int d=0;d<si;d++){
		int p=1+(j>=a[i][d].fi)+(k>=a[i][d].fi);
		if(a[i][d].se!=p)	return false;
	}
	return true;
}
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++){
		int l,r,x;
		scanf("%d%d%d",&l,&r,&x);
		a[r].push_back(make_pair(l,x));
	}
	f[0][0][0]=1;
	for(int i=0;i<n;i++)
		for(int j=0;j<=i;j++)
			for(int k=0;k<=j;k++)
				if(f[i][j][k]){
					if(!check(i,j,k)){
						f[i][j][k]=0;
						continue;
					}
					(f[i+1][j][k]+=f[i][j][k])%=P;
					if(!i)	continue;
					(f[i+1][i][k]+=f[i][j][k])%=P;
					if(!j)	continue;
					(f[i+1][i][j]+=f[i][j][k])%=P;
				}
	int ans=0;
	for(int i=0;i<=n;i++)
		for(int j=0;j<=i;j++)
			if(f[n][i][j]&&check(n,i,j)){
				if(i&&j)	ans=(ans+1LL*f[n][i][j]*6)%P;
				else	if(!i&&!j)	ans=(ans+1LL*f[n][i][j]*3)%P;
				else	ans=(ans+1LL*f[n][i][j]*6)%P;
			}
	printf("%d\n",ans);
	return 0;
}