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>
const int M = 2e5+10;

int f[M];
int d[M];

int find(int x) {
	if(f[x] == -1) return x;
	int fa = f[x];
	f[x] = find(fa);
	d[x] += d[fa];
	return f[x];
}

int main() {
	int n, m;
	scanf("%d%d", &n, &m);
	memset(f, -1, sizeof(f));
	bool flag = true;
	for(int i = 0; i < m; i ++) {
		int u, v, w;
		scanf("%d%d%d", &u, &v, &w);
		u --, v --;
		int fa = find(u);
		int fb = find(v);
		// printf("%d %d\n", fa, fb);
		if(fa == fb) {
			if(d[v]-d[u] != w) flag = false;
		} else {
			f[fb] = fa;
			d[fb] = d[u] - d[v] + w;
		}
	}
	if(flag) puts("Yes");
	else puts("No");
}