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:
import sys
sys.setrecursionlimit(10**5)
class UnionFind():
  def __init__(self, n):
    self.n = n
    self.root = [-1]*(n+1)
    self.rnk = [0]*(n+1)
    self.weight = [0]*(n+1)
  def Find_Root(self, x):
    if(self.root[x] < 0):
      return x
    else:
      r = self.Find_Root(self.root[x])
      self.weight[x] += self.weight[self.root[x]]
      self.root[x] = r
      return r
  def GetWeight(self, x):
    self.Find_Root(x)
    return self.weight[x]
  def Unite(self, x, y, w):
    w += self.GetWeight(x)
    w -= self.GetWeight(y)
    x = self.Find_Root(x)
    y = self.Find_Root(y)
    if(x == y):
      return False
    if self.rnk[x] < self.rnk[y]:
      x, y = y, x
      w = -w
    if self.rnk[x] == self.rnk[y]:
      self.rnk[x] += 1
    self.root[y] = x
    self.weight[y] = w
    return True
  def isSameGroup(self, x, y):
    return self.Find_Root(x) == self.Find_Root(y)
  def Count(self, x):
    return -self.root[self.Find_Root(x)]
  def Diff(self, x, y):
    return self.GetWeight(y) - self.GetWeight(x)
  
def main():
  N, M = map(int, input().split())
  lrd = [list(map(int, input().split())) for _ in range(M)]
  U = UnionFind(N)
  for i in range(M):
    l, r, d = lrd[i]
    if not U.isSameGroup(l, r):
      U.Unite(l, r, d)
    else:
      if U.Diff(l, r) != d:
        print('No')
        exit()
  print('Yes')
  
    
if __name__ == "__main__":
  main()