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 <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;

typedef pair <int, int> pii;

const int MAXN = 305;
const int MOD = 1000000007;

int N, M;
vector <pii> Q[MAXN];
int dp[MAXN][MAXN][MAXN];

void load() {
  scanf("%d%d", &N, &M);
  while (M--) {
    int l, r, x;
    scanf("%d%d%d", &l, &r, &x);
    Q[r].push_back(pii(l, x));
  }
}

inline int add(int x, int y) {
  x += y;
  if (x >= MOD)
    x -= MOD;
  return x;
}

int rec(int r, int g, int b) {
  int &ref = dp[r][g][b];
  if (ref != -1)
    return ref;
  ref = 0;
  if (r == g && r)
    return ref;
  if (g == b && g)
    return ref;
  if (b == r && b)
    return ref;
  int pos = max(max(r, g), b);
  for (int i = 0; i < Q[pos].size(); i++)
    if ((r >= Q[pos][i].first) + (g >= Q[pos][i].first) + (b >= Q[pos][i].first) != Q[pos][i].second)
      return ref;
  if (pos == N)
    return ref = 1;
  ref = add(ref, rec(pos + 1, g, b));
  ref = add(ref, rec(r, pos + 1, b));
  ref = add(ref, rec(r, g, pos + 1));
  return ref;
}

int solve() {
  memset(dp, -1, sizeof dp);
  return rec(0, 0, 0);
}

int main() {
  load();
  printf("%d\n", solve());
  return 0;
}