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 long long mod=1e9+7;
typedef pair<int,int> p;
int n,m;
long long ans=0,dp[310][310][310];
vector<p>vec[310];
void update(long long &x,long long y){x=(x+y)%mod;}
 
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1,l,r,x;i<=m;i++){
		scanf("%d%d%d",&l,&r,&x);
		vec[r].push_back(p(l,x));
	}
	dp[1][0][0]=1;
	for(int i=1;i<=n;i++){
		int t=vec[i].size()-1,l,x;
		for(int j=0;j<i;j++)
		  for(int k=0;k<=max(0,j-1);k++)
		    for(int p=0;p<=t;p++){
		    	l=vec[i][p].first;x=vec[i][p].second;
				if(x==1&&j>=l)dp[i][j][k]=0;
				else if(x==2&&(k>=l||j<l))dp[i][j][k]=0;
				else if(x==3&&k<l)dp[i][j][k]=0;
		    }
		for(int j=0;j<i;j++)
		  for(int k=0;k<=max(0,j-1);k++){
		  	dp[i+1][j][k]=(dp[i+1][j][k]+dp[i][j][k])%mod;
		  	dp[i+1][i][k]=(dp[i+1][i][k]+dp[i][j][k])%mod;
		  	dp[i+1][i][j]=(dp[i+1][i][j]+dp[i][j][k])%mod;
		  }
	}
	for(int i=0;i<n;i++)
	  for(int j=0;j<=max(0,i-1);j++)
	    ans=(ans+dp[n][i][j])%mod;
	printf("%lld",((ans+mod)%mod*3)%mod);
	return 0;
}