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:
#define _GLIBCXX_IOSTREAM
#include<bits/stdc++.h>
#define mod 1000000007
#define maxn 310
using namespace std;
typedef pair<int,int> par;
vector<par>v[maxn];
int n,m,dp[maxn][maxn][maxn];
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1,l,r,x;i<=m;++i)
		scanf("%d%d%d",&l,&r,&x),v[r].push_back(par(l,x));
	dp[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)if(dp[i][j][k]){
				int x=dp[i][j][k],y=max(i,max(j,k));
				for(int l=0;l<v[y].size();++l)
					if((i>=v[y][l].first)+(j>=v[y][l].first)+(k>=v[y][l].first)!=v[y][l].second)
						{dp[i][j][k]=0;goto nxt;}
				dp[y+1][j][k]=(dp[y+1][j][k]+x)%mod;
				dp[i][y+1][k]=(dp[i][y+1][k]+x)%mod;
				dp[i][j][y+1]=(dp[i][j][y+1]+x)%mod;
				nxt:;
			}
	int ans=0;
	for(int i=0;i<=n;++i)
		for(int j=0;j<=n;++j)
			ans=(1ll*ans+dp[i][j][n]+dp[i][n][j]+dp[n][i][j])%mod;
	printf("%d",ans);
}