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>

#define REP(i,a,b) for(int i=a,i##_end_=b;i<=i##_end_;++i)
#define pii pair<int,int>
#define fi first
#define se second
#define mk make_pair
typedef long long ll;

using namespace std;

void File(){
	freopen("ARC074E.in","r",stdin);
	freopen("ARC074E.out","w",stdout);
}

template<typename T>void read(T &_){
	T __=0,mul=1; char ch=getchar();
	while(!isdigit(ch)){
		if(ch=='-')mul=-1;
		ch=getchar();
	}
	while(isdigit(ch))__=(__<<1)+(__<<3)+(ch^'0'),ch=getchar();
	_=__*mul;
}

const int maxn=310;
const ll mod=1e9+7;
int n,m;
vector<pii>qu[maxn];
ll dp[maxn][maxn][maxn],ans;

void init(){
	read(n); read(m);
	int l,r,x;
	REP(i,1,m){
		read(l); read(r); read(x);
		qu[r].push_back(mk(l,x));
	}
}

void work(){
	dp[0][0][0]=1;
	REP(i,0,n)REP(j,0,n)REP(k,0,n){
		if((i && i==j) || (j && j==k) || (k && i==k))continue;
		int nex=max(i,max(j,k))+1,r=nex-1;
		bool flag=true;
		REP(f,0,qu[r].size()-1){
			int l=qu[r][f].fi,x=qu[r][f].se,cnt=0;
			if(i && i>=l)++cnt;
			if(j && j>=l)++cnt;
			if(k && k>=l)++cnt;
			if(cnt!=x){
				flag=false;
				dp[i][j][k]=0;
				break;
			}
		}
		if(!flag)continue;
		(dp[nex][j][k]+=dp[i][j][k])%=mod;
		(dp[i][nex][k]+=dp[i][j][k])%=mod;
		(dp[i][j][nex]+=dp[i][j][k])%=mod;
		if(r==n)(ans+=dp[i][j][k])%=mod;
	}
	printf("%lld\n",ans);
}

int main(){
	//File();
	init();
	work();
	return 0;
}