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:
def main():
    from collections import deque, defaultdict
    n, m = map(int, input().split())
    g = [[] for _ in range(n + 1)]
    ref = defaultdict(list)
    q = deque([])
    visited = set()
    inf = 10 ** 10
    dist = [-inf] * (n + 1)

    for i in range(m):
        a, b, k = map(int, input().split())
        g[a].append(b)
        g[b].append(a)
        ref[(a, b)] = k


    def dfs(u):
        q.append(u)
        while q:
            v = q.pop()
            visited.add(v)
            for x in g[v]:
                if x not in visited:
                    if ref[(v, x)] != []:
                        y = ref.get((v, x))
                        if dist[x] == -inf:
                            dist[x] = dist[v] + y
                        elif dist[x] != dist[v] + y:
                            print("No")
                            exit()
                    else:
                        y = ref.get((x, v))
                        if dist[x] == -inf:
                            dist[x] = dist[v] - y
                        elif dist[v] != dist[x] + y:
                            print("No")
                            exit()
                    q.append(x)


    for i in range(1, n + 1):
        if i not in visited:
            dist[i] = 1
            dfs(i)
    print("Yes")
if __name__ == '__main__':
    main()