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<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
#define int long long
const int mod=1000000007;
int f[310][310][310];
struct node{
	int l,x;
};
int n,m,l,r,x,ans;
vector<node>v[310];
bool check(int a,int b,int c){
	int r=max(max(a,b),c);
	for(int i=0;i<v[r].size();i++){
        int l=v[r][i].l,x=v[r][i].x,s=0;
        s=(a>=l)+(b>=l)+(c>=l);
        if(s!=x)return false;
    }
	return true;	
}
signed main(){
	scanf("%lld%lld",&n,&m);
	for(int i=1;i<=m;i++){
		scanf("%lld%lld%lld",&l,&r,&x);
		v[r].push_back((node){l,x});
	}
	f[0][0][0]=1;
	for(int i=0;i<=n;i++)
		for(int j=0;j<=n;j++)
			for(int k=0;k<=n;k++){
				r=max(max(i,j),k);
				if(i&&j&&i==j||i&&k&&i==k||j&&k&&j==k)continue;
				if(!check(i,j,k))f[i][j][k]=0;
				if(!f[i][j][k])continue;
				if(r==n){
					(ans+=f[i][j][k])%=mod;
					continue;
				}
				(f[r+1][j][k]+=f[i][j][k])%=mod;
				(f[i][r+1][k]+=f[i][j][k])%=mod;
				(f[i][j][r+1]+=f[i][j][k])%=mod;
			}
	printf("%lld\n",ans);
}