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 ll long long

const int N = 301;
const int mod = 1e9+7;

int add(int x,int y) {
   return (x+y)%mod;
}
int dp[N][N][N];

void make(int l,int r,int x) {
   for(int i=0;i<=r;++i) {
      for(int j = 0;j<=r;++j) {
         int cc = 1;
         if(l<=i) {
            ++cc;
         }
         if(l<=j) {
            ++cc;
         }
         if(cc != x) {
            dp[r][i][j] = dp[i][r][j] = dp[i][j][r] = 0;
         }
      }
   }
}
int solveDp(int r,int g,int b,int n) {
   int &ret = dp[r][g][b];
   if(ret!=-1) {
      return ret;
   }
   int ind = max(r,max(g,b)) +1;
   if(ind >n) {
      return ret = 1;
   }
   ret = add( solveDp(ind,g,b,n) ,add(solveDp(r,ind,b,n), solveDp(r,g,ind,n)));
   return ret;
}
void solve() {
   memset(dp,-1,sizeof(dp));
   int n,m;
   scanf("%d%d",&n,&m);
   for(int i=0;i<m;++i) {
      int l,r,x;
      scanf("%d%d%d",&l,&r,&x);
      make(l,r,x);
   }
   printf("%d\n", solveDp(0,0,0,n));
}
int main() {
   //freopen("input.txt","r",stdin);
   solve();
}