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 JAVA):

Solution:
// 勝手に変えてごめん！

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map.Entry;
 
public class Main
{
 
  static Integer[] x = new Integer[114514];
  static boolean used[] = new boolean[114514];
 
  public static void main(String[] args) throws IOException
  {
    BufferedReader r = new BufferedReader(new InputStreamReader(System.in), 1);
    String s = r.readLine();
    String[] sl = s.split("[\\s]+");
 
    int n = Integer.parseInt(sl[0]);
    int m = Integer.parseInt(sl[1]);
 
    HashMap<Integer, HashMap<Integer, Integer>> map = new HashMap<Integer, HashMap<Integer, Integer>>();
 
    for(int i = 0; i <= n; i++)
    {
      map.put(i, new HashMap<Integer, Integer>());
    }
 
    for(int i = 0; i < m; i++)
    {
      s = r.readLine();
      sl = s.split("[\\s]+");
      int left = Integer.parseInt(sl[0]);
      int right = Integer.parseInt(sl[1]);
      int dist = Integer.parseInt(sl[2]);
 
      HashMap<Integer, Integer> h = map.get(left);
      h.put(right, dist);
      h = map.get(right);
      h.put(left, - dist);
    }
 
    for(int i = 1; i <= n; i++)
    {
      x[i] = null;
    }
 
    for(int v = 1; v <= n; v++)
    {
      if(used[v]) continue;
      x[v] = 0;
      sub(map, v);
    }
 
 	/*
    for(int i = 1; i <= n; i++)
    {
      HashMap<Integer, Integer> h = map.get(i);
      for(Entry<Integer, Integer> e : h.entrySet())
      {
        if(x[e.getKey()] != x[i] + e.getValue())
        {
          System.out.println("No");
          System.exit(0);
        }
      }
    }
    */
 
    System.out.println("Yes");
 
  }
 
  public static void sub(HashMap<Integer, HashMap<Integer, Integer>> map, int i)
  {
    if(used[i]) return;
    used[i] = true;
    HashMap<Integer, Integer> h = map.get(i);
    for(Entry<Integer, Integer> e : h.entrySet())
    {
      if(x[e.getKey()] == null)
      {
        x[e.getKey()] = x[i] + e.getValue();
      	sub(map, e.getKey());
      }
      else
      {
        if(x[e.getKey()] != x[i] + e.getValue())
        {
          System.out.println("No");
          System.exit(0);
        }
      }
    }
  }
}