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 FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define FORD(i,b,a) for (int i = (int)(b) - 1; i >= a; --i)
#define REP(i,N) FOR(i,0,N)
#define st first
#define nd second
#define pb push_back

typedef pair<int, int> PII;
typedef long long LL;

int DP[305][305][305];
vector<PII> C[305];
const int MOD = 1000000007;

int main() {
  int N, M;
  scanf("%d%d", &N, &M);
  REP(i,M) {
    int l, r, x;
    scanf("%d%d%d", &l, &r, &x);
    C[r].pb({l, x});
  }

  DP[1][0][0] = 1;
  FOR(i,1,N+1) {
    if (i > 1) {
      REP(j,i)REP(k,i) {
        DP[i][j][k] = (DP[i][j][k] + DP[i-1][j][k]) % MOD;
        DP[i][i-1][k] = (DP[i][i-1][k] + DP[i-1][j][k]) % MOD;
        if (j > k) DP[i][i-1][j] = (DP[i][i-1][j] + DP[i-1][j][k]) % MOD;
      }
    }

    for (auto& p: C[i]) {
      REP(j,i)REP(k,i) if ((j >= p.st) + (k >= p.st) != p.nd - 1) DP[i][j][k] = 0;
    }
  }

  LL result = 0;
  REP(i,N)REP(j,N) {
    LL tmp = DP[N][i][j] * 3LL * (i == 0 ? 1 : 2);
    result += tmp;
  }
  printf("%d\n", (int)(result % MOD));
}