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 fi first
#define se second
#define sz(x) ((int)(x).size())
using namespace std;
using pii=pair<int,int>;

const int MOD=1e9+7;

int n,m,dp[2][301][301];
vector<pii> a[301];

int main() {
	scanf("%d%d",&n,&m);
	for(int i=0,l,r,v;i<m;i++) {
		scanf("%d%d%d",&l,&r,&v);
		a[r].push_back({l,v});
	}

	int cur=1,pr=0;
	dp[0][0][0]=1;
	
	for(int i=1;i<=n;i++) {
		for(int j=0;j<=i;j++) for(int k=0;k<=i;k++) dp[cur][j][k]=0;
		for(int j=0;j<i;j++) for(int k=0;k<i;k++) {
			dp[cur][j][k] = (dp[cur][j][k] + dp[pr][j][k])%MOD;
			dp[cur][i-1][j] = (dp[cur][i-1][j] + dp[pr][j][k])%MOD;
			dp[cur][i-1][k] = (dp[cur][i-1][k] + dp[pr][j][k])%MOD;
		}
		for(int j=0;j<i;j++)for(int k=0;k<i;k++) {
			for(auto &v:a[i]) {
				int c=1;
				if(j >= v.fi) c++; 
				if(k >= v.fi) c++;
				if(c!=v.se) dp[cur][j][k]=0;
			}
		}
		swap(cur,pr);
	}

	int ans=0;
	for(int j=0;j<n;j++) for(int k=0;k<n;k++) ans=(ans+dp[pr][j][k])%MOD;
	printf("%d\n",ans);
	
	return 0;
}