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;
const int maxn = 305;
typedef pair<int, int> pii;

vector<pii> qe[maxn];
int dp[maxn][maxn][maxn];
int n;

int perform(int r, int g, int b){
  int i = max(r, max(g, b));
  int & ans = dp[r][g][b];
  if(ans != -1){
    return ans;
  }
  ans = 0;
  for(pii q : qe[i]){
    int ct = 0;
    if(r >= q.first) ct++;
    if(g >= q.first) ct++;
    if(b >= q.first) ct++;
    if(ct != q.second) return ans;
  }
  if(i == n){
    ans = 1;
    return 1;
  }
  ans += perform(i+1, g, b); ans %= mod;
  ans += perform(r, i+1, b); ans %= mod;
  ans += perform(r, g, i+1); ans %= mod;
  return ans;
}

int main(){
  cin >> n;
  memset(dp, -1, sizeof(dp));
  int m;cin >> m;
  for(int i=0;i<m;i++){
    int l,r,x; cin >> l >> r >> x;
    qe[r].push_back(pii(l,x));
  }
  cout << perform(0, 0, 0) << "\n";
}