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;
typedef long long ll;
typedef pair<int,int>par;
ll f[305][305][305],ms=1e9+7;
int n,m;
vector<par>v[405];
int check(int r,int g,int b){
	int k=max(r,max(g,b));
	for (int i=0;i<v[k].size();i++){
		int cnt=0;
		int l=v[k][i].first,x=v[k][i].second;
		if (r>=l) cnt++;
		if (g>=l) cnt++;
		if (b>=l) cnt++;
		if (cnt!=x) return 0;
	}
	return 1;
}
int main(){
	scanf("%d%d",&n,&m);
	for (int i=1;i<=m;i++){
		int l,r,x; scanf("%d%d%d",&l,&r,&x);
		v[r].push_back(par(l,x));
	}
	f[0][0][0]=1; ll ans=0;
	for (int r=0;r<=n;r++){
		for (int g=0;g<=n;g++){
			for (int b=0;b<=n;b++){
				if (f[r][g][b]==0) continue;
				if (check(r,g,b)==0){
					f[r][g][b]=0; continue;
				}
				int p=max(r,max(g,b))+1;
				if (p==n+1) ans=(ans+f[r][g][b])%ms;
				f[p][g][b]=(f[p][g][b]+f[r][g][b])%ms;
				f[r][p][b]=(f[r][p][b]+f[r][g][b])%ms;
				f[r][g][p]=(f[r][g][p]+f[r][g][b])%ms;
			}
		}
	}
	printf("%lld\n",ans);
	return 0;
}