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:
# D
from collections import deque
N, M = map(int, input().split())

value_list = [0]*N
done_list = [-1]*N
# -1:any, 0:not_done, 1:done

res = 'Yes'

G = dict()
for i in range(N):
    G[i] = dict()
    
# input
for _ in range(M):
    L, R, D = map(int, input().split())
    G[L-1][R-1] = D
    G[R-1][L-1] = -D
    done_list[L-1] = 0
    done_list[R-1] = 0

# pick one node not resolved
pick = 0

while pick < N and res == 'Yes':
    
    queue = deque([pick])
    done_list[pick] = 1
    value_list[pick] = 0
    
    # BFS
    while len(queue) > 0:
        L = queue.popleft()
        for R in G[L].keys():
            if done_list[R] == 0:
                done_list[R] = 1
                value_list[R] = value_list[L] + G[L][R]
                queue.append(R)
            else:
                if value_list[R] != value_list[L] + G[L][R]:
                    res = 'No'

    # next seed
    while pick < N:
        if done_list[pick] == 0:
            break
        pick += 1
print(res)