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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

from collections import deque

n,m=map(int,input().split())
edge=[[] for _ in range(n)]
for i in range(m):
    l,r,d=map(int,input().split())
    edge[l-1].append((r-1,d))
    edge[r-1].append((l-1,-d))

top=[False]*n

for i in range(n):
    memo=[False]*n
    if top[i]:
        l=deque([(i,top[i])])
        memo[i]=top[i]
    else:
        l=deque([(i,0)])
        memo[i]=0
    while l:
        now=l.popleft()
        for to in edge[now[0]]:
            if memo[to[0]]:
                if top[to[0]]:
                    if top[to[0]]==to[1]+memo[now[0]]:
                        continue
                    else:
                        print("No")
                        exit()
                else:
                    top[to[0]]=to[1]+memo[now[0]]
            else:
                if top[to[0]]:
                    if top[to[0]]==to[1]+memo[now[0]]:
                        memo[to[0]]=top[to[0]]
                    else:
                        print("No")
                        exit()
                else:
                    memo[to[0]]=to[1]+memo[now[0]]
                    top[to[0]]=to[1]+memo[now[0]]
            l.append((to[0],memo[to[0]]))


print("Yes")