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 mod = 1e9+7;

long long int dp[302][302][302];

void add(long long int&x, long long int y){
	x=(x+y)%mod;
}

vector<pair<int,int> > event[301];
int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n,m,k;
	cin>>n>>m;
	for(int i=1,l,r,x;i<=m;i++){
		cin>>l>>r>>x;
		event[r].push_back(make_pair(l,x));
	}
	dp[0][0][0]=1;
	for(int r=0;r<=n;r++)
		for(int g=0;g<=n;g++)
			for(int b=0;b<=n;b++){
				k=max(r,max(g,b));
				for(auto it:event[k]){
					if((r>=it.first)+(b>=it.first)+(g>=it.first)!=it.second)
						dp[r][g][b]=0;
				}
				add(dp[k+1][g][b],dp[r][g][b]);
				add(dp[r][k+1][b],dp[r][g][b]);
				add(dp[r][g][k+1],dp[r][g][b]);
			}
	long long int ans=0;
	for(int r=0;r<=n;r++)
		for(int g=0;g<=n;g++)
			for(int b=0;b<=n;b++)
				if(r==n||b==n||g==n)
					add(ans,dp[r][g][b]);
	cout<<ans<<endl;
}