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;
#define N 333
#define mod 1000000007

int n,m,f[N][N][N],ans;
vector<pair<int,int> > q[N];

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

int read(){
	int x=0,f=1;char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-')  f=-f;
	for (;isdigit(ch);ch=getchar()) x=x*10+ch-'0';
	return x*f;
}

int main(){
	n=read();m=read();
	for (int i=1;i<=m;i++){
		int x=read(),y=read(),z=read();
		q[y].push_back(make_pair(x,z));
	}
	f[1][0][0]=3;
	for (int i=0;i<=n;i++)
		for (int j=0;j<=n;j++)
			for (int k=0;k<=n;k++){
				for (int l=0;l<(int)q[i].size();l++)
					if (1+(j>=q[i][l].first)+(k>=q[i][l].first)!=q[i][l].second) f[i][j][k]=0;
				if (i==n) pls(ans,f[i][j][k]);
				else pls(f[i+1][j][k],f[i][j][k]),
					pls(f[i+1][i][k],f[i][j][k]),
					pls(f[i+1][i][j],f[i][j][k]);
			}
	printf("%d\n",ans);
	return 0;
}