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 pb push_back
#define fi first
#define se second

using namespace std;
typedef pair<int,int> pi;

const int N=305,P=1e9+7;

int n,m,dp[N][N][N],ans;
vector<pi> e[N];

int main(){
	scanf("%d%d",&n,&m);
	for(int i=1,l,r,x;i<=m;i++)scanf("%d%d%d",&l,&r,&x),e[r].pb({l,x});
	dp[0][0][0]=1;
	for(int i=1;i<=n;i++){
		for(int j=0;j<i;j++)for(int k=0;k<=j;k++)
			if(int w=dp[i-1][j][k]){
				(dp[i][j][k]+=w)%=P;
				(dp[i][i-1][k]+=w)%=P;
				(dp[i][i-1][j]+=w)%=P;
			}
		for(auto v:e[i]){
			for(int j=0;j<i;j++)for(int k=0;k<=j;k++)
				if(dp[i][j][k]){
					int c=(j>=v.fi)+(k>=v.fi)+1;
					if(c!=v.se)dp[i][j][k]=0;
				}
		}
	}
	for(int j=0;j<n;j++)for(int k=0;k<=j;k++)
		if(dp[n][j][k])(ans+=dp[n][j][k])%=P;
	printf("%d\n",ans);
	return 0;
}