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 <vector>
#include <iostream>
typedef std::pair<int,int> pii;

int n,m,Ans,f[305][305][305];
std::vector<pii> e[305];
const int p=1000000007;

inline void Inc(int &x,int y){if((x+=y)>=p)x-=p;}

int main()
{
    scanf("%d%d",&n,&m),f[1][0][0]=3;
    for(int l,r,x;m--;)scanf("%d%d%d",&l,&r,&x),e[r].push_back(pii(l,x));
    for(int i=1;i<=n;++i)
        for(int j=0;j<i;++j)
            for(int k=j;k<i;++k)
            {
                for(pii x:e[i])
                    if(x.second==1)k>=x.first?f[i][j][k]=0:0;
                    else if(x.second==2)(k<x.first||j>=x.first)?f[i][j][k]=0:0;
                    else if(j<x.first)f[i][j][k]=0;
                if(i==n)Inc(Ans,f[i][j][k]);
                Inc(f[i+1][j][k],f[i][j][k]);
                Inc(f[i+1][j][i],f[i][j][k]);
                Inc(f[i+1][k][i],f[i][j][k]);
            }
    return printf("%d\n",Ans),0;
}