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;

constexpr int mod = 1e9 + 7;

struct segment {
    int l, x;
    segment(int a, int b) : l(a), x(b) {}
};

int n, m;
vector<segment> seg[301];
int dp[301][301][301];

bool check(int r, int g, int b) {
    const int rp = max({r, g, b});
    for(auto const& s : seg[rp]) {
        const int cnt = (s.l <= r) + (s.l <= g) + (s.l <= b);
        if(cnt != s.x) return false;
    }
    return true;
}

int solve(int r, int g, int b) {
    if(g >= b) swap(g, b);
    if(r >= g) swap(r, g);
    if(g >= b) swap(g, b);

    int& res = dp[r][g][b];
    if(res != -1) return dp[r][g][b];
    if(!check(r, g, b)) return dp[r][g][b] = 0;
    if(b == n) return dp[r][g][b] = 1;
    res = 0;
    (res += solve(b + 1, g, b)) %= mod;
    (res += solve(r, b + 1, b)) %= mod;
    (res += solve(r, g, b + 1)) %= mod;
    return res;
}

int main() {
    memset(dp, -1, sizeof(dp));

    cin >> n >> m;
    for(int i = 0; i < m; ++i) {
        int l, r, x; cin >> l >> r >> x;
        seg[r].emplace_back(l, x);
    }

    cout << solve(0, 0, 0) << endl;
}