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=round(1e9)+7;
int f[302][302][302],i,l,r,k,n,m;
struct pt { int l,k; };
vector <pt> vec[302];
bool check(int v1,int v2,int v3)
{
    int i=max(v1,max(v2,v3));
    for(int j=0;j<vec[i].size();j++)
    {
        int l=vec[i][j].l,k=vec[i][j].k;
        int t=(v1>=l)+(v2>=l)+(v3>=l);
        if(t!=k) return 0;
    }
    return 1;
}
int tinh(int v1,int v2,int v3)
{
    if(f[v1][v2][v3]>-1) return f[v1][v2][v3];
    if(check(v1,v2,v3)==0) return f[v1][v2][v3]=0;
    int i=max(v1,max(v2,v3))+1;
    if(i>n) return 1;
    int kq=0;
    kq=(kq+tinh(i,v2,v3))%mod;
    kq=(kq+tinh(v1,i,v3))%mod;
    kq=(kq+tinh(v1,v2,i))%mod;
    return f[v1][v2][v3]=kq;
}
int main()
{
   // freopen("ntu.inp","r",stdin);
   // freopen("ntu.out","w",stdout);
    cin>>n>>m;
    for(i=1;i<=m;i++)
    {
        cin>>l>>r>>k;
        vec[r].push_back({ l,k });
    }
    memset(f,-1,sizeof(f));
    cout<<tinh(0,0,0);
}