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:
from collections import deque

class Edge:
	def __init__(self, t, w):
		self.to = t
		self.ew = w

class Graph:
	def __init__(self, N):
		self.nw = [-1] * N
		self.al = [[] for i in range(N)]

	def add_edge(self, fr, to, weight):
		self.al[fr].append(Edge(to, weight))
		self.al[to].append(Edge(fr, -weight))

	def dfs(self, s, used):
		self.nw[s] = 0
		q = deque([s])
		used.add(s)
		while q:
			h = q.popleft()
			for e in self.al[h]:
				if e.to in used:
					if self.nw[h] + e.ew != self.nw[e.to]:
						return False
					continue
				used.add(e.to)
				self.nw[e.to] = self.nw[h] + e.ew
				q.appendleft(e.to)
		return True


def main():
	N, M = map(int, input().split())
	graph = Graph(N)
	for i in range(M):
		l, r, d = map(int, input().split())
		graph.add_edge(l - 1, r - 1, d)

	used = set()
	for i in range(N):
		if i in used or graph.dfs(i, used):
			continue
		print("No")
		break
	else:
		print("Yes")


if __name__ == "__main__":
	main()