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:
import sys
sys.setrecursionlimit(10**5)
N,M = map(int, input().split())
input = sys.stdin.readline
LRD = [ [int(j) for j in input().split()] for _ in range(M)]

data = [x for x in range(N+1)]
rank = [0]  * (N+1)
diff_weight = [0] * (N+1)

def root(x):
    if data[x] == x:
        return x
    else:
        r = root( data[x] )
        diff_weight[x] += diff_weight[ data[x] ]
        data[x] = r
        return r

def weight(x):
    # _ = root(x)
    return diff_weight[x]


def diff(x,y):
    return weight(y) - weight(x)

def merge(x,y,w):
    w  += weight(x); w -= weight(y)
    x = root(x)
    y = root(y)
    if x == y: return False
    if rank[x] < rank[y]: x,y = y,x; w = -w
    if rank[x] == rank[y]: rank[x] += 1
    data[y] = x
    diff_weight[y] = w
    return True

def issame(x,y):
    return root(x) == root(y)

for i in range(M):
    L,R,D = LRD[i]
    # print(L,R,D)
    if not issame(L,R):
        _  = merge(L,R,D)
    else:
        if diff(L,R) != D:
            print("No")
            exit(0)
            
print("Yes")