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;
long long dp[305][305][305],l,r,x,n,m,mod;
vector<pair<int,int> > a[305];
long long dq(int i,int v1,int v2,int v3)
{
    if (dp[v1][v2][v3]!=-1) return dp[v1][v2][v3];
    bool kt=true;
    int l,mau;
    for (int j=0;j<a[i-1].size();++j)
    {
        l=a[i-1][j].first;
        mau=a[i-1][j].second;
        if (v1>=l) mau--;
        if (v2>=l) mau--;
        if (v3>=l) mau--;
        if (mau!=0) {kt=false;break;}
    }
    if (!kt) return dp[v1][v2][v3]=0;
    if (i>n) return 1;

    long long k=(dq(i+1,i,v2,v3)+dq(i+1,v1,i,v3)+dq(i+1,v1,v2,i))%mod;
    return dp[v1][v2][v3]=k;

}
int main()
{
   
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    cin>>n>>m;mod=1000000007;
    for (int i=1;i<=m;++i)
    {
        cin>>l>>r>>x;
        a[r].push_back({l,x});
    }
    memset(dp,-1,sizeof(dp));
    cout<<dq(1,0,0,0);

    return 0;
}