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 <iostream>
#include <vector>
#define MOD 1000000007
#define REP(i,a,n)for(int i=(a);i<=(n);i++)
#define ADDMOD(a, b) (a)=((a)+(b))%MOD
using namespace std;
typedef pair<int, int> pii;

int N,M,L,R,X;
vector<pii> Q[301];
int dp[301][301][301];

bool check(int m, int i, int j) {
  int mi=min(i,j),mx=max(i,j);
  for(pii p : Q[m]) {
    int l=p.first,x=p.second;
    if(x==1 && !(mx < l)) return false;
    if(x==2 && !(mi < l && l <= mx)) return false;
    if(x==3 && !(l <= mi)) return false;
  }
  return true;
}

int main(void) {
  cin>>N>>M;
  REP(i,1,M) {
    cin>>L>>R>>X;
    Q[R].push_back(pii(L,X));
  }

  REP(i,0,N) REP(j,0,N) REP(k,0,N) dp[i][j][k]=0;
  dp[0][0][0]=1;

  REP(i,0,N-1) REP(j,0,N-1) REP(k,0,N-1) if(dp[i][j][k] > 0) {
    int m=max(i,max(j,k))+1;
    if(check(m,j,k)) ADDMOD(dp[m][j][k], dp[i][j][k]);
    if(check(m,k,i)) ADDMOD(dp[i][m][k], dp[i][j][k]);
    if(check(m,i,j)) ADDMOD(dp[i][j][m], dp[i][j][k]);
  }

  long ans=0;
  REP(i,0,N-1) REP(j,0,N-1) {
    ADDMOD(ans, dp[N][i][j]);
    ADDMOD(ans, dp[i][N][j]);
    ADDMOD(ans, dp[i][j][N]);
  }
  cout<<ans<<endl;

  return 0;
}