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 JAVA):

Solution:
import java.util.ArrayList;
import java.util.Scanner;

public class Main {
	public static void main(String[] args){

		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int n = sc.nextInt();
		int m = sc.nextInt();



		ArrayList<Integer> ss = new ArrayList<>();
		ArrayList<Integer> tt = new ArrayList<>();

		for(int i=0;i<m;i++) {
			ss.add(sc.nextInt());
			tt.add(sc.nextInt());
		}

		int[][] st = new int[n+1][n];

		for(int i=1;i<n+1;i++) {
			int counter =0;
			for(int j=0;j<ss.size();j++) {
				if(ss.get(j)==i) {
					counter++;
					st[i][counter]=tt.get(j);
				}
			}
			st[i][0]=counter;
		}

		double[] p = new double[n+1];

		double min =700;

		for(int i =1;i<n;i++) {//どこからの枝を狩るか

			for(int j =0;j<n+1;j++) {
				p[j]=0;
			}
			for(int j=n-1;j>0;j--) {//動的計画法

				double max = 0;
				int maxIndex = -1;
				if(i==j&&st[j][0]!=1) {//


					for(int k=1;k<st[j][0]+1;k++) {
						if(p[st[j][k]]>max) {
							max = p[st[j][k]];
							maxIndex = k;
						}
					}

				}

				for(int k=1;k<st[j][0]+1;k++) {
					if(maxIndex==-1) {
						if(k!=maxIndex)p[j]+=(p[st[j][k]]+1.0)*(1.0/st[j][0]);
					}else {
						if(k!=maxIndex)p[j]+=(p[st[j][k]]+1.0)*(1.0/(st[j][0]-1));
					}
				}

			}
			if(min>p[1])min=p[1];
		}




		//String s = sc.next();

		//String[] ss = s.split("");

		//int[] a = new int[n];


		double ans = min;

		System.out.println(ans);

		/*
		TreeMap<Integer,Integer> treeMap = new TreeMap<>();//sorted no duplication
		treeMap.put(b[n], n);
		*/

	}

}
/*
class City{
	int order;
	int prefecture;
	int year;
	int number;
	City(int order,int prefecture, int year){
		this.order = order;
		this.prefecture = prefecture;
		this.year = year;
	}
}
*/