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 find(x, U, r, w): #x: ノード名、U:前のノードの配列 w:前のノードからの距離の配列、r:深さ
  if x == U[x]:
    return (x, w[x])
  else:
    k = find(U[x], U, r, w)
    #付け替え処理
    w[x] += w[U[x]]
    U[x] = k[0]
    #print(k)
    return (U[x],w[x])

def merge(a, b, U, r, w, w_add): #w_add　aにbを付け加える時、距離をwはなす
  a = find(a, U, r, w)[0]
  b = find(b, U, r, w)[0]
  if a == b:#何もしない
    return  
  """
  if r[a] < r[b]:
    a, b = b, a #a（深い）にb（浅い）をくっつける
  U[b] = a  
  if r[a] == r[b]:#もともと同じ深さの時だけ、結合後の深さが１増えるため
    r[a] += 1
  """
  U[b] = a
  r[a] = max(r[a], r[b]+1)
  w[b] += w_add
  return

N, M = map(int,input().split())
U = [i for i in range(N)]#前のノード（自分が先頭の時は自分の値）
w = [0 for _ in range(N)]#前のノードとの距離
r = [0 for _ in range(N)]#自分の木の深さ（自分が先頭の時のみ）

ans = True
for _ in range(M):
  
  L, R, D = map(int,input().split())
  L -= 1
  R -= 1
  t1 = find(L, U, r, w)
  t2 = find(R, U, r, w)
  #print(U,w)
  if t1[0] == t2[0] and not(t2[1] - t1[1] == D):
    ans = False 
    break
  if not(t1[0] == t2[0]):
    D -= t2[1] - t1[1]
    if r[L] < r[R]:
      L, R = R, L
      D = -D
    merge(L, R, U, r, w, D)
  
print("Yes" if ans else "No")