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:
N, M = map(int, input().split())
xval = [float("INF")]*(N+1)
road = {}
for i in range(1, N+1):
    road[i] = {}
for i in range(M):
    r, l, d = map(int, input().split())
    road[r][l] = d
    road[l][r] = -d

checked = set()
i = 1
while len(checked) < N:
    for j in range(i, N+1):
        if j in checked:
            continue
        else:
            i = j
            checked.add(i)
            break
    xval[i] = 0
    check = set([i])
    while len(check) > 0:
        nextcheck = set()
        for x in check:
            for y in road[x].keys():
                if xval[y] == float("INF"):
                    xval[y] = xval[x] + road[x][y]
                    checked.add(y)
                    nextcheck.add(y)
                else:
                    if xval[y] != xval[x] + road[x][y]:
                        print("No")
                        exit()
                    else:
                        continue
        check = nextcheck
print("Yes")