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.
have = False
cycle_begin, block_u, block_v = -1, -1, -1
g, mark, cycle = [], [], []


def dfs(u):
    global have, cycle_begin
    mark[u] = 1
    for v in g[u]:
        if u == block_u and v == block_v:
            continue
        if mark[v] == 0:
            if dfs(v):
                if have:
                    cycle.append(u)
                if u == cycle_begin:
                    have = False
                return True
        elif mark[v] == 1:
            have = True
            cycle_begin = v
            cycle.append(u)
            return True
    mark[u] = 2
    return False


n, m = map(int, input().split())

g = [[] for _ in range(n)]
mark = [0 for _ in range(n)]

for _ in range(m):
    u, v = map(int, input().split())
    u -= 1
    v -= 1
    g[u].append(v)

for i in range(n):
    if mark[i] == 0 and dfs(i):
        break

if cycle_begin == -1:
    print("YES")
else:
    cycle.append(cycle[0])
    for u in range(len(cycle) - 1, 0, -1):
        block_u = cycle[u]
        block_v = cycle[u - 1]
        mark = [0 for _ in range(n)]
        ok = True
        for u in range(n):
            if mark[u] == 0 and dfs(u):
                ok = False
                break
        if ok:
            print("YES")
            exit()

    print("NO")
