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;

const int mod = 1e9 + 7;
int N, M;
vector< pair< int, int > > ev[300];
int dp[301][301][301];

bool check(int r, int g, int b)
{
  for(auto &e : ev[max({r, g, b})]) {
    int sz = 0;
    sz += e.first <= r;
    sz += e.first <= g;
    sz += e.first <= b;
    if(sz != e.second) return (false);
  }
  return (true);
}

int rec(int r, int g, int b)
{
  int &ret = dp[r + 1][g + 1][b + 1];
  int nxt = max({r, g, b}) + 1;
  if(~ret) return (ret);
  if(nxt == N) return (ret = 1);
  ret = 0;
  if(check(nxt, g, b)) (ret += rec(nxt, g, b)) %= mod;
  if(check(r, nxt, b)) (ret += rec(r, nxt, b)) %= mod;
  if(check(r, g, nxt)) (ret += rec(r, g, nxt)) %= mod;
  return (ret);
}

int main()
{
  cin >> N >> M;
  for(int i = 0; i < M; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    --a, --b;
    ev[b].emplace_back(a, c);
  }
  memset(dp, -1, sizeof(dp));
  cout << rec(-1, -1, -1) << endl;
}