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 For(i,a,b) for(int i=a;i<=b;i++)
#define maxn 303
#define maxm 303
#define pb push_back
#define MOD 1000000007
using namespace std;
long long dp[maxn][maxn][maxn];
typedef pair<int,int> ii;
vector<ii> cond[maxm];
int main(){
	int N,M,a,b,c;
	cin >> N >> M;
	For(i,1,M){
		cin >> a >> b >> c;
		cond[b].pb(ii(a,c));
	}
//	cout << "--";
	long long ans = 0;
	dp[0][0][0] = 1;
	For(i,0,N){
		For(j,0,N){
			For(k,0,N){
				int r = max(i,max(j,k));
				For(t,1,cond[r].size()){
					int l = cond[r][t-1].first;
					int v = cond[r][t-1].second;
					int numColor = (i>=l)+(j>=l)+(k>=l);	
					if(numColor != v){
						dp[i][j][k] = 0;
						break;
					}
				}			
				if(dp[i][j][k] == 0)	continue;
				if(r==N) {
					ans = (ans+ dp[i][j][k])%MOD;
					continue;
				}
				(dp[r+1][j][k] += dp[i][j][k]) %= MOD;
				(dp[i][r+1][k] += dp[i][j][k]) %= MOD;
				(dp[i][j][r+1] += dp[i][j][k]) %= MOD;
			}
		}
	}
	cout << ans;
}