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:
from collections import Counter, defaultdict
import sys
sys.setrecursionlimit(10 ** 5 + 10)
input = sys.stdin.readline
from math import factorial
import heapq, bisect
import math

def calc(A, B, C, now_t):
    ans = A * now_t + B * math.sin(C * now_t * math.pi)
    return ans


def main():
    num, hint_num = map(int, input().split())
    data = [list(map(int, input().split())) for i in range(hint_num)]

    graph_data = defaultdict(set)
    dist_data = defaultdict(int)

    for i in range(hint_num):
        l, r , d = data[i]
        graph_data[l].add(r)
        graph_data[r].add(l)
        dist_data[(l, r)] = d
        dist_data[(r, l)] = -1 * d


    position = ['x' for i in range(num + 1)]
    flg = 1
    for i in range(1, num + 1):
        if position[i] != 'x':
            continue
        position[i] = 0
        now_set = set()
        next_set = set()
        now_set.add(i)

        while len(now_set) > 0:
            for now_ele in now_set:
                for next_ele in graph_data[now_ele]:
                    length = dist_data[(now_ele, next_ele)]
                    if position[next_ele] == 'x':
                        position[next_ele] = position[now_ele] + length
                        next_set.add(next_ele)
                    else:
                        if position[next_ele] != position[now_ele] + length:
                            flg = 0
                            break
            now_set = next_set
            next_set = set()

    # print(position)

    if flg:
        print('Yes')
    else:
        print('No')





if __name__ == '__main__':
    main()