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<iostream>
#include<algorithm>
#include<vector>
using namespace std;
const int maxn=307;
const int MOD=1000000007;
struct data{
	int l,x;
};
int n,m,ll,rr,xx,f[maxn][maxn][maxn],ans;
vector <data> a[maxn];
bool check(int r,int g,int b){
	int k=max(max(r,g),b);
	for (int i=0; i<a[k].size(); i++) {
		data now=a[k][i];
		int cnt=0;
		int left=now.l;
		if (r>=left) ++cnt;
		if (g>=left) ++cnt;
		if (b>=left) ++cnt;
		if (cnt!=now.x) return false;
	}
	return true;
}
int main(){
	ios::sync_with_stdio(false);
	cin>>n>>m;
	for (int i=1; i<=m; i++) {
		cin>>ll>>rr>>xx;
		data tmp;
		tmp.l=ll; tmp.x=xx;
		a[rr].push_back(tmp);
	} 
	f[0][0][0]=1;
	for (int r=0; r<=n; r++)
		for (int g=0; g<=n; g++)
			for (int b=0; b<=n; b++) {
				int c=f[r][g][b];
				if (!c) continue;
				if (!check(r,g,b)) {f[r][g][b]=0; continue;}
				int k=max(max(r,g),b)+1;
				if (k==n+1) ans=(ans+f[r][g][b]) % MOD;
				f[k][g][b]=(f[k][g][b]+f[r][g][b]) % MOD;
				f[r][k][b]=(f[r][k][b]+f[r][g][b]) % MOD;
				f[r][g][k]=(f[r][g][k]+f[r][g][b]) % MOD;
			} 
	cout<<ans<<endl;
	return 0;
}