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 resolve():

    N,M = map(int,input().split())
    root = list(range(N))
    depth = [1 for _ in range(N)]
    dist = [0 for _ in range(N)]

    def find(a,root,dist):
        if root[a] == a:
            return (a,0)
        else:
            root[a],d = find(root[a],root,dist)
            dist[a] += d
            return(root[a],dist[a])

    def unite(a,b,d,root,depth,dist):
        A,dist_a = find(a,root,dist)
        B,dist_b = find(b,root,dist)
        if A == B:
            if dist_b - dist_a == d:
                return True
            else:
                return False
        else:
            if depth[A] > depth[B]:
                root[B] = A
                depth[A] += depth[B]
                dist[B] = dist_a - dist_b + d
            else:
                root[A] = B
                depth[B] += depth[A]
                dist[A] = dist_b - dist_a - d
            return True
        
    ans = True
    for _ in range(M):
        L,R,D = map(int,input().split())
        if not (unite(L-1,R-1,D,root,depth,dist)):
            ans = False
            break
    print("Yes" if ans else "No")
resolve()