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:
vs = set()
from collections import defaultdict
def dfs_w(d, stack):
    depthh = defaultdict(int)
    path = [0]
    pvs = set()
    if stack[0] in vs:
        return True
    while stack:
        v, dpd = stack.pop()
        if v > 0:
            parent = path[-1]
            path.append(v)
            vs.add(v)
            pvs.add(v)
            depthh[v] = depthh[parent] + dpd

            for u, dpd in d[v]:
                if u in pvs:
                    if depthh[u] != depthh[v] + dpd:
                        return False
                if u in vs:
                    continue
                stack += [(-v, dpd), (u, dpd)]
        else:
            path.pop()

    return True
#    return S, F, depth, depthh

if __name__ == '__main__':
    N, M = map(int, input().split())
    G = [set() for _ in range(N+1)]
    for _ in range(M):
        a, b, c = map(int, input().split())
        G[a].add((b,c))
        G[b].add((a,-c))
    for i in range(N):
        if i in vs:
            continue
        stack = [(i+1, 0)] 
        r =  dfs_w(G, stack)
        if not r:
            break
    if r:
        print("Yes")
    else:
        print("No")