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 (3.8.2) (judge verdict: Time Limit Exceeded)

def topo_sort(g):
    from collections import deque
    V = len(g)
    deg = [0]*V
    for src in range(V):
        for dst in g[src]:
            deg[dst] += 1
    ans = list(v for v in range(V) if deg[v]==0)
    deq = deque(ans)
    used = [0]*V

    while deq:
        v = deq.popleft()
        for t in g[v]:
            deg[t] -= 1
            if deg[t]==0:
                deq.append(t)
                ans.append(t)
    return ans

def resolve():
    N, M = list(map(int, input().split()))
    LRD = [list(map(int, input().split())) for _ in range(M)]
    adj_list = [[] for _ in range(N)]
    adj_matrix = [[None for _ in range(N)] for __ in range(N)]
    for lrd in LRD:
        l, r, d = lrd
        adj_list[l-1].append(r-1)
        adj_matrix[l-1][r-1] = d
    
    #top_order = topological_sort(adj_list)
    top_order = topo_sort(adj_list)
    
    if len(top_order) != len(adj_list):
        print("No")
        return
    
    acc = 0
    start = top_order[0]
    now = top_order[0]
    for i in range(1, len(top_order)):
        nxt = top_order[i]
        if adj_matrix[now][nxt] is not None:
            if adj_matrix[start][nxt] is not None and acc+adj_matrix[now][nxt] != adj_matrix[start][nxt]:
                print("No")
                return
            acc += adj_matrix[now][nxt]
        now = nxt
        
    print("Yes")


if '__main__' == __name__:
    resolve()