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 <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <utility>
#define FR first
#define SE second
#define MOD 1000000007

using namespace std;

typedef pair<int,int> pr;

int f[2][305][305];

inline void update(int &x,int y) {
  x=(x+y)%MOD;
}

vector <pr> vt[305];

bool check(int x,int y,int z) {
  for(int i=0;i<vt[x].size();i++) {
  	pr t=vt[x][i];
    if ((x>=t.FR)+(y>=t.FR)+(z>=t.FR)!=t.SE) return 0;
  }
  return 1;
}

int dp(int n) {
  int cur=0;
  f[0][0][0]=1;
  for(int i=0;i<n;i++) {
    cur^=1;
    memset(f[cur],0,sizeof(f[cur]));
    for(int j=0;j<=i;j++)
    for(int k=0;k<=j;k++)
    if (f[cur^1][j][k]) {
    	if (check(i+1,j,k)) update(f[cur][j][k],f[cur^1][j][k]);
    	if (check(i+1,i,k)) update(f[cur][i][k],f[cur^1][j][k]);
    	if (check(i+1,i,j)) update(f[cur][i][j],f[cur^1][j][k]);
	}
  }
  int ans=0;
  for(int i=0;i<=n;i++)
    for(int j=0;j<=n;j++) update(ans,f[cur][i][j]);
  return ans;
}

int main() {
  int n,m;
  scanf("%d%d",&n,&m);
  for(int i=1;i<=m;i++) {
  	int x,y,z;
  	scanf("%d%d%d",&x,&y,&z);
  	vt[y].push_back(pr(x,z));
  }
  printf("%d\n",dp(n));
  return 0;
}