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 N 305
using namespace std;
const int mod=1e9+7; 
int dp[2][N][N];
int n,m;
vector<pair<int,int> > L[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);
		L[r].push_back(make_pair(x,l));
	}
	int now=0;
	dp[now][0][0]=1;
	for(int i=1;i<=n;i++){
		memset(dp[now^1],0,sizeof(dp[0]));
		for(int j=0;j<i;j++)
			for(int k=0;k<=j;k++){
				if(dp[now][j][k]==0) continue;
				bool fl=true;
				for(int l=0;l<L[i].size()&&fl;l++)
					if(L[i][l].first==1){
						fl&=j<L[i][l].second;
					}else if(L[i][l].first==2){
						fl&=j>=L[i][l].second&&k<L[i][l].second;
					}else{
						fl&=k>=L[i][l].second;
					}
				if(!fl) {dp[now][j][k]=0;continue;}
				(dp[now^1][j][k]+=dp[now][j][k])%=mod;
				(dp[now^1][i][k]+=dp[now][j][k])%=mod;
				if(j!=k) (dp[now^1][i][j]+=dp[now][j][k])%=mod;
			}
		now^=1;
	}
	now^=1;
	long long ans=dp[now][0][0]*3;
	for(int i=1;i<n;i++)
		for(int j=0;j<i;j++)
			ans+=dp[now][i][j]*6LL;
	cout<<ans%mod<<endl;
	return 0;
}