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 il inline
#define vd void
#define mod 1000000007
typedef long long ll;
il int gi(){
	int x=0,f=1;
	char ch=getchar();
	while(!isdigit(ch)){
		if(ch=='-')f=-1;
		ch=getchar();
	}
	while(isdigit(ch))x=x*10+ch-'0',ch=getchar();
	return x*f;
}
int f[310][310][310];
struct pr{int l,x;};
std::vector<pr>A[310];
il bool check(int x,int a,int b){
	for(int i=0;i<A[x].size();++i)
		if(1+(a>=A[x][i].l)+(b>=A[x][i].l)!=A[x][i].x)
			return 0;
	return 1;
}
int main(){
	int n=gi(),m=gi(),l,r,x;
	for(int i=1;i<=m;++i)l=gi(),r=gi(),x=gi(),A[r].push_back((pr){l,x});
	f[0][0][0]=1;
	for(int i=0;i<n;++i)
		for(int j=0;j<=i;++j)
			for(int k=0;k<=i;++k){
				if(check(i+1,j,k))(f[i+1][j][k]+=f[i][j][k])%=mod;
				if(check(i+1,i,k))(f[i+1][i][k]+=f[i][j][k])%=mod;
				if(check(i+1,i,j))(f[i+1][i][j]+=f[i][j][k])%=mod;
			}
	int ans=0;
	for(int i=0;i<=n;++i)
		for(int j=0;j<=n;++j)
			(ans+=f[n][i][j])%=mod;
	printf("%d\n",ans);
	return 0;
}