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 root(v):
    if par[v] == v:
        return v
    r = root(par[v])
    diff_weight[v] += diff_weight[par[v]]
    par[v] = r
    return r

def weight(v):
    root(v)
    return diff_weight[v]

def diff(u, v):
    return weight(v) - weight(u)

def unite(u, v, w):
    w += diff(v, u)
    u = root(u)
    v = root(v)
    if u == v:
        return
    if rank[u] < rank[v]:
        u, v = v, u
        w = -w
    par[v] = u
    diff_weight[v] = w
    if rank[u] == rank[v]:
        rank[u] += 1

def same(u, v):
    return root(u) == root(v)

N, M = map(int, input().split())
par = list(range(N))
rank = [0] * N
diff_weight = [0] * N
for _ in range(M):
    l, r, d = map(int, input().split())
    l -= 1
    r -= 1
    if same(l, r):
        dist = diff(l, r)
        if dist != d:
            print("No")
            exit()
    else:
        unite(l, r, d)

print("Yes")