You are given a [directed graph](https://en.wikipedia.org/wiki/Directed_graph) consisting of n vertices and m edges (each edge is directed, so it can be traversed in only one direction). You are allowed to remove at most one edge from it.

Can you make this graph [acyclic](https://en.wikipedia.org/wiki/Directed_acyclic_graph) by removing at most one edge from it? A directed graph is called acyclic iff it doesn't contain any cycle (a non-empty path that starts and ends in the same vertex).

Input

The first line contains two integers n and m (2 ≤ n ≤ 500, 1 ≤ m ≤ min(n(n - 1), 100000)) — the number of vertices and the number of edges, respectively.

Then m lines follow. Each line contains two integers u and v denoting a directed edge going from vertex u to vertex v (1 ≤ u, v ≤ n, u ≠ v). Each ordered pair (u, v) is listed at most once (there is at most one directed edge from u to v).

Output

If it is possible to make this graph acyclic by removing at most one edge, print YES. Otherwise, print NO.

Examples

Input

3 4
1 2
2 3
3 2
3 1


Output

YES


Input

5 6
1 2
2 3
3 2
3 1
2 1
4 5


Output

NO

Note

In the first example you can remove edge <image>, and the graph becomes acyclic.

In the second example you have to remove at least two edges (for example, <image> and <image>) in order to make the graph acyclic.
import sys


def prepare():
    stack = [i for i in range(n) if deg[i] == 0]
    cnt = 0
    while stack:
        v = stack.pop()
        cnt += 1
        for dest in adj[v]:
            deg[dest] -= 1
            if deg[dest] == 0:
                stack.append(dest)
        adj[v].clear()

    return cnt == n


def solve(st):
    stack = [st]
    visited = [0]*n
    cnt = 0
    while stack:
        v = stack.pop()
        cnt += 1
        for dest in adj[v]:
            if dest == st:
                continue
            visited[dest] += 1
            if deg[dest] == visited[dest]:
                stack.append(dest)

    return cnt == m


n, m = map(int, sys.stdin.buffer.readline().decode('utf-8').split())
adj = [[] for _ in range(n)]
rev = [[] for _ in range(n)]
deg = [0]*n
for u, v in (map(int, line.decode('utf-8').split()) for line in sys.stdin.buffer):
    adj[u-1].append(v-1)
    rev[v-1].append(u-1)
    deg[v-1] += 1

ok = prepare()
if ok:
    print('YES')
    exit()

m = len([1 for i in range(n) if deg[i] > 0])
for i in range(n):
    if deg[i] == 1 and solve(i):
        print('YES')
        exit()

print('NO')
