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 CPP):

Solution:
#include <cstdio>

const int N = 100000;

int n, m, p[N], d[N];

int find(int u)
{
    if (p[u] == u) {
        return u;
    }
    int r = find(p[u]);
    d[u] += d[p[u]];
    p[u] = r;
    return r;
}

int main()
{
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; ++ i) {
        p[i] = i, d[i] = 0;
    }
    while (m --) {
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c);
        a --;
        b --;
        int pa = find(a);
        int pb = find(b);
        if (pa == pb) {
            if (d[b] - d[a] != c) {
                puts("No");
                return 0;
            }
        } else {
            p[pb] = pa;
            d[pb] = c - d[b] + d[a];
        }
    }
    puts("Yes");
}