Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

from collections import defaultdict, deque
import sys

readline = sys.stdin.buffer.readline

N, M = map(int, readline().split())
dic = defaultdict(list)
par = [i for i in range(N)]
rank = [0]*N
def find(x):
  if par[x]==x:
    return x
  else:
    par[x] = find(par[x])
    return par[x]
def unit(x, y):
  x = find(x)
  y = find(y)
  if x==y:
    return
  elif rank[x]<rank[y]:
    par[x] = y
    return
  elif rank[y]<rank[x]:
    par[y] = x
  else:
    par[y] = x
    rank[x] += 1

for i in range(M):
  l, r, d = map(int, readline().split())
  dic[l-1] += [(r-1,d)]
  dic[r-1] += [(l-1,-d)]
  unit(l-1, r-1)


dist = [-1]*N
for x in range(N):
  x = find(x)
par = set(par)
stuck = deque([])
for c in par:
  stuck += [(c,0)]
  dist[c] = 0
while stuck:
  e, a = stuck.popleft()
  flag = False
  for c in dic[e]:
    p, d = c
    x = d + dist[e]
    if dist[p]==-1:
      dist[p] = x
      stuck += [(p, x)]
    elif dist[p]!=x:
      print('No')
      flag = True
      break
  if flag:
    break
else:
  print('Yes')