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 <algorithm>
#include <vector>

#define Rep(i, n) for (int i = 1; i <= n; i ++)
#define Rep0(i, n) for (int i = 0; i <= n; i ++)
#define mp(a, b) make_pair(a, b)

using namespace std;

typedef pair<int, int> pii;
const int N = 310;
const int mod = 1e9 + 7;

int f[N][N][N], g[N][4];

void inc(int &a, int b) { a = (a + b) % mod;}

vector<pii> tt[N];

int main()
{
	int n, m;
	scanf("%d%d", &n, &m);
	Rep(i, m) {
		int l, r, c;
		scanf("%d%d%d", &l, &r, &c);
		l += 3, r += 3;
		tt[r].push_back(mp(l, c));
	}
	
	f[3][2][1] = 1;
	
	int ans = 0;
	
	for (int i = 3; i <= n + 3; i ++)
		Rep(j, i - 1) Rep(k, j - 1) {
			bool flag = false;
			for (int h = 0; h < tt[i].size(); h ++){
				pii tmp = tt[i][h];
				if (tmp.second == 1 && tmp.first <= j) flag = true; 
				else if (tmp.second == 2 && (tmp.first > j || tmp.first <= k)) flag = true;
				else if (tmp.second == 3 && tmp.first > k) flag = true;
			}
			if (flag) continue;
			if (i < n + 3){
				inc(f[i + 1][j][k], f[i][j][k]);
				inc(f[i + 1][i][j], f[i][j][k]);
				inc(f[i + 1][i][k], f[i][j][k]);
			}
			else inc(ans, f[i][j][k]);
		}
	printf("%d\n", ans);
	
	return 0;
}