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 Nmax = int(1e5 + 2);
int n, m, val[Nmax];
bool vis[Nmax];
vector<pair<int, int>>G[Nmax];
void dfs(int x) {
   vis[x] = 1;
   for(auto it : G[x]) {
      int y = it.first, cost = it.second;
      if(!vis[y]) {
         val[y] = val[x] + cost;
         dfs(y);
      } else if(val[y] != val[x] + cost) {
         cout << "No";
         exit(0);
      }
   }
}
int32_t main() {
  //ifstream cin("a.in");
   cin >> n >> m;
   for(int i = 1; i <= m; ++i) {
      int l, r, c;
      cin >> l >> r >> c;
      G[l].emplace_back(r, c);
      G[r].emplace_back(l, -c);
   }
   for(int i = 1; i <= n; ++i)
      if(!vis[i]) dfs(i);
   cout << "Yes";
}