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 <cstring>
#include <algorithm>
#include <vector>
using namespace std;
typedef long long ll;
const int maxn = 305, mod = 1000000007;
#define rep(i, s, t) for(int i=s, tt=t; i<=tt; ++i)
int N, M;
int f[maxn][maxn][maxn];
vector<pair<int,int> > lm[maxn];
bool check(int r, int g, int b, int l, int x) {
    return (r >= l) + (g >= l) + (b >= l) == x;
}
int che(int r, int g, int b, int k) {
    for(int i = 0; i < (int)lm[k].size(); ++i)
	if(!check(r, g, b, lm[k][i].first, lm[k][i].second))
	    return f[r][g][b] = 0;
    return f[r][g][b];
}
int main() {
    scanf("%d%d", &N, &M);
    for(int i = 1, l, r, x; i <= M; ++i) {
	scanf("%d%d%d", &l, &r, &x);
	lm[r].push_back(make_pair(l, x));
    }
    int ans = 0;
    f[0][0][0] = 1;
    rep(i, 0, N) rep(j, 0, N) rep(k, 0, N) {
	int r = max(i, max(j, k));
	if(!che(i, j, k, r)) continue;
	(f[r + 1][j][k] += f[i][j][k]) %= mod;
	(f[i][r + 1][k] += f[i][j][k]) %= mod;
	(f[i][j][r + 1] += f[i][j][k]) %= mod;
	if(r == N) ans = (ans + f[i][j][k]) % mod;
    }
    printf("%d\n", ans);
    return 0;
}
// r g b