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 maxn=300+10;
const int mod=1e9+7;
int n,m,f[maxn][maxn][maxn],ans;

struct Limit{
	int l,x;
};

vector<Limit> v[maxn];

int check(int a,int b,int c){
	int r=max(a,max(b,c)),cnt;Limit p;
	for(int i=0;i<v[r].size();i++){
		p=v[r][i];
		cnt=(p.l<=a)+(p.l<=b)+(p.l<=c);
		if(cnt!=p.x) return 0;
	}
	return 1;
}

int main()
{
	scanf("%d%d",&n,&m);
	int l,r,x;
	for(int i=1;i<=m;i++){
		scanf("%d%d%d",&l,&r,&x);
		v[r].push_back((Limit){l,x});
	}
	f[0][0][0]=1;
	int p;
	for(int i=0;i<=n;i++)
		for(int j=0;j<=n;j++)
			for(int k=0;k<=n;k++){
				if(!f[i][j][k]) continue;
				p=max(i,max(j,k));
				if(!check(i,j,k)){
					f[i][j][k]=0;
					continue;
				}
				if(p==n) ans=(ans+f[i][j][k])%mod;
				f[p+1][j][k]=(f[p+1][j][k]+f[i][j][k])%mod;
				f[i][p+1][k]=(f[i][p+1][k]+f[i][j][k])%mod;
				f[i][j][p+1]=(f[i][j][p+1]+f[i][j][k])%mod;
			}
	/*for(int i=0;i<=n;i++)
		for(int j=0;j<=n;j++)
			for(int k=0;k<=n;k++)
				printf("dp[%d][%d][%d]=%d\n",i,j,k,f[i][j][k]);*/
	printf("%d\n",ans);
    return 0;
}