Problem: There is a cave consisting of N rooms and M one-directional passages. The rooms are numbered 1 through N.

Takahashi is now in Room 1, and Room N has the exit. The i-th passage connects Room s_i and Room t_i (s_i < t_i) and can only be traversed in the direction from Room s_i to Room t_i. It is known that, for each room except Room N, there is at least one passage going from that room.

Takahashi will escape from the cave. Each time he reaches a room (assume that he has reached Room 1 at the beginning), he will choose a passage uniformly at random from the ones going from that room and take that passage.

Aoki, a friend of Takahashi's, can block one of the passages (or do nothing) before Takahashi leaves Room 1. However, it is not allowed to block a passage so that Takahashi is potentially unable to reach Room N.

Let E be the expected number of passages Takahashi takes before he reaches Room N. Find the value of E when Aoki makes a choice that minimizes E.

Constraints

* 2 \leq N \leq 600
* N-1 \leq M \leq \frac{N(N-1)}{2}
* s_i < t_i
* If i != j, (s_i, t_i) \neq (s_j, t_j). (Added 21:23 JST)
* For every v = 1, 2, ..., N-1, there exists i such that v = s_i.

Input

Input is given from Standard Input in the following format:


N M
s_1 t_1
:
s_M t_M


Output

Print the value of E when Aoki makes a choice that minimizes E. Your output will be judged as correct when the absolute or relative error from the judge's output is at most 10^{-6}.

Examples

Input

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


Output

1.5000000000


Input

3 2
1 2
2 3


Output

2.0000000000


Input

10 33
3 7
5 10
8 9
1 10
4 6
2 5
1 7
6 10
1 4
1 3
8 10
1 5
2 6
6 9
5 6
5 8
3 6
4 8
2 7
2 9
6 7
1 2
5 9
6 8
9 10
3 9
7 8
4 5
2 10
5 7
3 5
4 7
4 9


Output

3.0133333333

Solution (in PYTHON3):

Solution:
"""
References
----------
[0]. 解説(公式), https://img.atcoder.jp/abc144/editorial.pdf, AtCoder
    - O(NM)
[1]. kmjp. AtCoder ABC #144 : F - Fork in the Road, <http://kmjp.hatenablog.jp/entry/2019/10/28/0930>, kmjp's blog
    - O(NM)
[2]. physics0523. Fork in the Road(ABC144-F), <https://physics0523.hatenablog.com/entry/2019/10/27/235334>, physics0523's 精進ログ
    - O(M)
[3]. Genki Ogaki. BC144 F - Fork in the Road考察＋参戦記, <https://www.onakasuitacity.com/abc144-f>, おじさん、今日プロ始
めるってよ
    - O(M)
"""
def solve(n, m, s, t):
    edges = [[] for i in range(n)]
    for i in range(m):
        u, v = s[i], t[i]
        edges[u-1].append(v-1)
    p = [0] * n
    p[0] = 1
    for i in range(n):
        for j in edges[i]:
            p[j] += p[i] / len(edges[i])
    E = [0] * n
    for i in range(n-2, -1, -1):
        v = [E[j] for j in edges[i]]
        E[i] = 1 + sum(v) / len(v)
    res = E[0]
    for i in range(n):
        deg = len(edges[i])
        if deg <= 1:
            continue
        k = max((E[j], j) for j in edges[i])[1]
        v = [E[j] for j in edges[i] if j != k]
        res = min(res, E[0] + p[i] * (sum(v) / (deg-1) - E[k]) / deg)
    return res

n, m = map(int, input().split())
s = [0] * m
t = [0] * m
for i in range(m):
    s[i], t[i] = map(int, input().split())
print(solve(n, m, s, t))