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<cstdio>
#include<algorithm>
#define MAX 200005
using namespace std;

struct A{ int par; int dis; }; 
A a[MAX];

void getp(int x){
  if(a[x].par != x){
    getp(a[x].par);
    a[x].dis += a[a[x].par].dis;
    a[x].par = a[a[x].par].par;
  }
}

int main(){
  int n, m, l, r, d, i;
  bool flag = true;
  scanf("%d%d", &n, &m);
  for(i = 1; i <= n; i++){
    a[i].par = i;
    a[i].dis = 0;
  }
  for(i = 0; i < m; i++){
    scanf("%d%d%d", &l, &r, &d);
    getp(l);
    getp(r);
    if(a[l].par == a[r].par){
      if(a[r].dis - a[l].dis != d) flag = false;
    }else{
      a[a[r].par].dis = -a[r].dis + d + a[l].dis;
      a[a[r].par].par = a[l].par;
    }
  }
  if(flag) printf("Yes\n");
  else printf("No\n");
}