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 PYTHON3):

Solution:
def ascend(anc, union, dist, rec):
	count = 0
	while anc != union[anc]:
		rec[count] = anc
		anc = union[anc]
		count += 1
	rec[count] = anc
	for i in range(count - 1, -1, -1):
		dist[rec[i]] += dist[rec[i + 1]]
		union[rec[i]] = anc
	return anc

def connect(l, r, d, union, dist, rec):
	l_anc = ascend(l, union, dist, rec)
	r_anc = ascend(r, union, dist, rec)
	if l_anc != r_anc:
		union[l_anc] = r_anc
		dist[l_anc] = dist[r] + d - dist[l]

def is_union(l, r, union, dist, rec):
	return ascend(l, union, dist, rec) == ascend(r, union, dist, rec)

def main():
	N, M = map(int, input().split())
	union = list(range(N + 1))
	dist = [0] * (N + 1)
	rec = [0] * (N + 1)
	for i in range(M):
		l, r, d = map(int, input().split())
		if is_union(l, r, union, dist, rec):
			if dist[r] + d != dist[l]:
				print("No")
				break
		else:
			connect(l, r, d, union, dist, rec)
	else:
		print("Yes")

if __name__ == "__main__":
	main()