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: Wrong Answer)

import sys
read = sys.stdin.buffer.read
input = sys.stdin.buffer.readline
inputs= sys.stdin.buffer.readlines
#rstrip().decode('utf-8')

#import math
#import numpy as np
#import operator
#import bisect
#from heapq import heapify,heappop,heappush
#from math import gcd
#from fractions import gcd
#from collections import deque
#from collections import defaultdict
#from collections import Counter
#from itertools import accumulate
#from itertools import groupby
#from itertools import permutations
#from itertools import combinations
#from scipy.sparse import csr_matrix
#from scipy.sparse.csgraph import floyd_warshall
#from scipy.sparse.csgraph import csgraph_from_dense
#from scipy.sparse.csgraph import dijkstra
#sys.setrecursionlimit(10**7)

#map(int,input().split())

def main():
	n,m=map(int,input().split())
	li=[[] for i in range(n+1)]
	for i in range(m):
		l,r,d=map(int,input().split())
		li[l].append((r,d))
		#li[r].append((l,-d))
	
	stack=[]
	check=set()
	a=[-10**10]*(n+1)
	
	for i in range(1,n+1):
		if li[i]==[""] or (i in check):
			continue
		else:
			stack.append(i)
			a[i]=0
			while stack:
				now=stack.pop()
				check.add(now)
				for j in li[now]:
					if j[0] in check:
						if a[j[0]]-a[now]!=j[1]:
							print("No")
							exit(0)
						else:
							continue
					if j[0] in stack:
						continue
					a[j[0]] = a[now] + j[1]
					stack.append(j[0])
					
	print("Yes")
	
	
if __name__ == '__main__':
	main()