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;
#define ll long long
typedef pair<int,int> pi;
#define f first
#define s second
#define FAST ios_base::sync_with_stdio(0); cin.tie(0);
#define all(x) x.begin(),x.end()
const int maxn = 305;
const int mod = 1e9+7;

int n,m;
bool fails[maxn][maxn][maxn];
int dp[maxn][maxn][maxn]; //RGB

int dpf(int R, int G, int B) {
	if (dp[R][G][B] != -1) return dp[R][G][B];
	int x = R, y = G, z = B;
	if (z > y) swap(z,y);
	if (y > x) swap(x,y);
	if (z > y) swap(z,y);
	
	if (fails[x][y][z]) return dp[R][G][B] = 0;
	if (x == n) return 1;
	
	dp[R][G][B] = dpf(x+1,G,B);
	
	dp[R][G][B] += dpf(R,x+1,B);
	dp[R][G][B] %= mod;
	
	dp[R][G][B] += dpf(R,G,x+1);
	dp[R][G][B] %= mod;
	
	return dp[R][G][B];
}

int main() {
	FAST
	cin >> n >> m;
	
	for (int xd =0;xd<m;xd++) {
		int a,b,x; cin >> a >> b >> x;
		for (int i =0;i<=n;i++) {
			for (int j=0;j<=i;j++) {
				int co = 1;
				if (i >= a) co++;
				if (j >= a) co++;
				
				if (co != x) fails[b][i][j] = 1;
			}
		}
	}
	memset(dp,-1,sizeof dp);
	cout << dpf(0,0,0);
	
}