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;
using lint = long long int;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T> void assign(V<T>& v, int n, const T& a = T()) { v.assign(n, a); }
template<class T, class... U> void assign(V<T>& v, int n, const U&... u) { v.resize(n); for (auto&& i : v) assign(i, u...); }

const lint mod = 1e9 + 7;
inline lint emod(lint a, lint p = mod) { return (a % p + p) % p; }

int main() {
  cin.tie(NULL); ios::sync_with_stdio(false);
  int n, m; cin >> n >> m;
  struct cond { int l, r, x; };
  VV<cond> cs(n + 1);
  for (int i = 0; i < m; i++) {
    int l, r, x; cin >> l >> r >> x, l--;
    cs[r].push_back({l, r, x});
  }
  auto f = [&](cond c, int j, int k) {
    if (c.x == 1) return j <= c.l;
    if (c.x == 2) return k <= c.l and c.l < j;
    if (c.x == 3) return c.l < k;
  };
  VV<V<>> dp; assign(dp, n + 1, n, n);
  dp[0][0][0] = 1;
  for (int i = 0; i < n; i++) for (int j = 0; j <= i; j++) for (int k = 0; k <= j; k++) {
    bool ok = true;
    for (auto&& c : cs[i + 1]) if (!f(c, j, k)) ok = false;
    if (ok) (dp[i + 1][j][k] += dp[i][j][k]) %= mod;
    ok = true;
    for (auto&& c : cs[i + 1]) if(!f(c, i, k)) ok = false;
    if (ok) (dp[i + 1][i][k] += dp[i][j][k]) %= mod;
    ok = true;
    for (auto&& c : cs[i + 1]) if(!f(c, i, j)) ok = false;
    if (ok) (dp[i + 1][i][j] += dp[i][j][k]) %= mod;
  }
  lint res = 0;
  for (int j = 0; j < n; j++) for (int k = 0; k <= j; k++) (res += dp[n][j][k]) %= mod;
  cout << emod(res) << '\n';
}