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(4100000)

def func(array, arr, d):
  for v in arr:
    if array[v[0]] == None:
      d1 = d + v[1]
      array[v[0]] = d1
      arr1 = dic.get(v[0], [])
      
      if not func(array, arr1, d1):
        return False
      
    elif array[v[0]] != d + v[1]:
      return False
    
  return True
      

n,m = map(int, input().split())

array = [None] * n
dic = {}

for i in range(m):
  l,r,d = map(int, input().split())
  l -= 1
  r -= 1
  
  dic.setdefault(l,[])
  dic.setdefault(r,[])
  dic[l].append((r,d))
  dic[r].append((l,-d))
  
for i in range(n):
  if array[i] != None:
    continue
    
  array[i] = 0
  arr = dic.get(i, [])
  
  if not func(array, arr, 0):
    print('No')
    sys.exit()

print('Yes')