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;

using ll = long long;
using vi = vector<int>;
using db = double;
#define pb push_back

const int mxn = 306;
const ll mod = 1E9+7;
const int MXL = 0x3f3f3f3f;

int n, m;
ll f[mxn][mxn][mxn];
int mn[mxn][4];
int mx[mxn][4];

bool check(int i, int j, int k) {
	#define ass(x) ({if(!(x))return false;})
	ass(j < mn[i][1]);
	ass(k < mn[i][2] && mx[i][2] <= j);
	ass(mx[i][3] <= k);
	
	return true;
}

int main() {
	cin >> n >> m;
	for (int i = 1; i <= n; ++i)
		for (int j = 1; j <= 3; ++j) {
			mn[i][j] = MXL;
			mx[i][j] = -MXL;
		}
	for (int i = 0; i < m; ++i) {
		int l, r, w;
		cin >> l >> r >> w;
		mn[r][w] = min(mn[r][w], l);
		mx[r][w] = max(mx[r][w], l);
	}
	
	f[1][0][0] = 3 % mod;
	
	for (int i = 1; i <= n; ++i)
		for (int j = 0; j < i; ++j)
			for (int k = 0; k < j || k == 0; ++k) {
				if (check(i, j, k)) {
					(f[i + 1][j][k] += f[i][j][k]) %= mod;
					(f[i + 1][i][k] += f[i][j][k]) %= mod;
					(f[i + 1][i][j] += f[i][j][k]) %= mod;
				} else {
					f[i][j][k] = 0;
				}
			}
	
	ll ans = 0;
	
	int i = n;
	for (int j = 0; j < i; ++j)
		for (int k = 0; k < j || k == 0; ++k)
			(ans += f[i][j][k]) %= mod;
	
	cout << ans << endl;
	
	return 0;
}