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 ll long long 
using namespace std;
const int mod=1e9+7;
inline int rd(){
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-') f=0;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+(ch^48);ch=getchar();}
	return f?x:-x;
}
inline void add(int &x,int y){
	x+=y;
	if(x>=mod) x-=mod;
}
int f[305][305][305],n,m,k,L,R,ans;
vector<int>g[305][4];
inline void update(int p){
	for(int i=1;i<=3;i++){
		for(int j=g[p][i].size()-1,l;j>=0;j--){
			l=g[p][i][j];
			for(int a=0;a<=p;a++){
				for(int b=0;b<=p;b++){
					for(int c=(a<p&&b<p)?p:0;c<=p;c++){
						if((a>=l)+(b>=l)+(c>=l)!=i) f[a][b][c]=0; 
					}
				}
			}
		}
	}
}
void work(){
	f[0][0][0]=1;
	for(int i=1;i<=n;i++){
		for(int j=0;j<i;j++){
			for(int l=0,now;l<i;l++){
				for(int u=(j<i-1&&l<i-1)?i-1:0;u<i;u++){
					now=f[j][l][u];
					add(f[i][l][u],now);
					add(f[j][i][u],now);
					add(f[j][l][i],now);
				}
			}
		}
		update(i);
	}
	for(int j=0;j<=n;j++){
		for(int l=0;l<=n;l++){
			for(int u=(j<n&&l<n)?n:0;u<=n;u++){
				add(ans,f[j][l][u]);
			}
		}
	}
}
int main(){
	n=rd(),m=rd();
	for(int i=1;i<=m;i++){
		L=rd(),R=rd(),k=rd();
		g[R][k].push_back(L);
	}
	work();
	cout<<ans;
	return 0;
}