Small sequence and the first n elements

Small sequence and the first n elements

Description

Given two ordered list of length n (non-descending table) A and B, in taking an addition of any of the respective A and B, and a n2 can be obtained. These and find the smallest n

Input

Is input two lines, each row has n integers, separated with a space between each other.

Output

Output the contents of only one line, the line has n is an integer of from small to large, and the n representatives obtained, with a space between each other.

Sample Input

1 3 5 7
2 4 6 8

Sample Output

3 5 5 7

HINT

30% of the data, 1≤n≤1000; 100% of the data, 1≤n≤100000; all data, 2n number entered between -109 to 109;

Source