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:
class UF():
  def __init__(self, N):
    self.parents = [-1] * (N+1)
    self.weight = [0] * (N+1)

  def union(self, f, t, w):
    w += self.weight[f]
    w -= self.weight[t]

    p1 = self.find(f)
    p2 = self.find(t)
    if p1 == p2:
      return

    if self.parents[p1] > self.parents[p2]:
      p1,p2 = p2,p1
      w = -w
    self.parents[p1] += self.parents[p2]
    self.weight[p2] = w
    self.parents[p2] = p1

  def find(self, x):
    if self.parents[x] < 0:
      return x
    else:
      y = self.find(self.parents[x])
      self.weight[x] += self.weight[self.parents[x]]
      self.parents[x] = y
      return y

  def compare_weight(self, x, y):
    self.find(x); self.find(y)
    return abs(self.weight[y] - self.weight[x])

  def same(self, n1, n2):
    # import pdb; pdb.set_trace()
    return self.find(n1) == self.find(n2)

N,M = map(int, input().split())
uf = UF(N)
flg = True
for _ in range(M):
  l,r,d = map(int, input().split())
  if uf.same(l, r):
    if uf.compare_weight(l,r) != d:
      flg = False
      break
  else:
    uf.union(l,r,d)

print('Yes') if flg else print('No')