Roads not only in Berland

Description:

Input:

The first line contains integer n (2 ≤ n ≤ 1000) — amount of cities in Berland and neighboring countries. Next n - 1 lines contain the description of roads. Each road is described by two space-separated integers a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i) — pair of cities, which the road connects. It can't be more than one road between a pair of cities. No road connects the city with itself.

Output:

Output the answer, number t — what is the least amount of days needed to rebuild roads so that from each city it became possible to reach all the others. Then output t lines — the plan of closure of old roads and building of new ones. Each line should describe one day in the format i j u v — it means that road between cities i and j became closed and a new road between cities u and v is built. Cities are numbered from 1. If the answer is not unique, output any.

Sample Input:

2
1 2

Sample Output:

0

Sample Input:

7
1 2
2 3
3 1
4 5
5 6
6 7

Sample Output:

1
3 1 3 7