Problem: There are N people standing on the x-axis. Let the coordinate of Person i be x_i. For every i, x_i is an integer between 0 and 10^9 (inclusive). It is possible that more than one person is standing at the same coordinate.

You will given M pieces of information regarding the positions of these people. The i-th piece of information has the form (L_i, R_i, D_i). This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.

It turns out that some of these M pieces of information may be incorrect. Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.

Constraints

* 1 \leq N \leq 100 000
* 0 \leq M \leq 200 000
* 1 \leq L_i, R_i \leq N (1 \leq i \leq M)
* 0 \leq D_i \leq 10 000 (1 \leq i \leq M)
* L_i \neq R_i (1 \leq i \leq M)
* If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).
* D_i are integers.

Input

Input is given from Standard Input in the following format:


N M
L_1 R_1 D_1
L_2 R_2 D_2
:
L_M R_M D_M


Output

If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print `Yes`; if it does not exist, print `No`.

Examples

Input

3 3
1 2 1
2 3 1
1 3 2


Output

Yes


Input

3 3
1 2 1
2 3 1
1 3 5


Output

No


Input

4 3
2 1 1
2 3 5
3 4 2


Output

Yes


Input

10 3
8 7 100
7 9 100
9 8 100


Output

No


Input

100 0


Output

Yes

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

const int N = 1e5 + 5;
const long long inf = 1e18;

long long dp[N];
vector<pair<int, int>> edge[N];

bool dfs(int now, long long cost) {
  if (dp[now] != inf) return dp[now] == cost;
  dp[now] = cost;
  for (auto it : edge[now]) {
    if (dfs(it.first, cost + it.second) == 0) {
      return 0;
    }
  }
  return 1;
}

int main() {
  int n, m;
  scanf("%d %d", &n, &m);
  for (int i = 0; i < m; i++) {
    int l, r, d;
    scanf("%d %d %d", &l, &r, &d);
    edge[l].emplace_back(r, d);
    edge[r].emplace_back(l, -d);
  }
  fill(dp, dp + N, inf);
  for (int i = 1; i <= n; i++) {
    if (dp[i] == inf) {
      if (dfs(i, 0) == 0) {
        puts("No");
        return 0;
      }
    }
  }
  puts("Yes");
  return 0;
}