Problem:
Score : 800 points

Problem Statement

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.

Sample Input 1

3 1
1 3 3

Sample Output 1

6

The six ways are:

RGB

RBG

GRB

GBR

BRG

BGR

where R, G and B correspond to red, green and blue squares, respectively.

Sample Input 2

4 2
1 3 1
2 4 2

Sample Output 2

6

The six ways are:

RRRG

RRRB

GGGR

GGGB

BBBR

BBBG

Sample Input 3

1 3
1 1 1
1 1 2
1 1 3

Sample Output 3

0

There are zero ways.

Sample Input 4

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

Sample Output 4

108

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>

using namespace std;
#define X first
#define Y second
#define pb push_back
typedef double db;
typedef long long ll;
typedef pair<int,int> P;
const int MAXN=305,MOD=1e9+7;
vector<P> inc[MAXN];
int n,m,l,r,x,dp[MAXN][MAXN][MAXN],res;

bool check(int x,int y,int z)
{
    int cur=max(x,max(y,z));
    for(auto t:inc[cur])
    {
        int l=t.X,op=t.Y,cnt=0;
        cnt=(x>=l)+(y>=l)+(z>=l);
        if(cnt!=op) return false;
    }
    return true;
}

int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++)
        scanf("%d%d%d",&l,&r,&x),inc[r].pb(P(l,x));
    dp[0][0][1]=dp[0][1][0]=dp[1][0][0]=1;
    for(int i=0;i<=n;i++)
        for(int j=0;j<=n;j++)
            for(int k=0;k<=n;k++)
            {
                if((i==j&&i&&j)||(i==k&&i&&k)||(j==k&&j&&k)) continue;
                // cout<<i<<" "<<j<<" "<<k<<" "<<dp[i][j][k]<<endl;
                if(!check(i,j,k)) dp[i][j][k]=0;
                if(!dp[i][j][k]) continue;
                
                int cur=max(i,max(j,k));
                if(cur==n) (res+=dp[i][j][k])%=MOD;
                (dp[cur+1][j][k]+=dp[i][j][k])%=MOD;
                (dp[i][cur+1][k]+=dp[i][j][k])%=MOD;
                (dp[i][j][cur+1]+=dp[i][j][k])%=MOD;
            }
    printf("%d",res);
    return 0;
}