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;

typedef long long LL;

int N,M;
int fa[200010],d[200010];

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

int main()
{
	scanf("%d%d",&N,&M);
	for (int i=1;i<=N;i++)fa[i] = i, d[i] = 0;
	bool ok = true;
	for (int i=1;i<=M;i++)
	{
		int L,R,D;
		scanf("%d%d%d",&L,&R,&D);
		if (find(L) == find(R))
		{
			if (d[L] - d[R] != D) ok = false;
		}
		else
		{
			int fl = find(L), fr = find(R);
			d[fl] = D + d[R] - d[L];
			fa[fl] = fr;
		}
	}
	if (ok)
		puts("Yes");
	else
		puts("No");
	
}