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Swap elements

Given two arrays, you are asked if it’s possible to make those arrays equal by swapping at most one pair of elements. Those elements can be from one array, or one element can be from the first one, while the other from the second one.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 1000), the number of elements in each of the arrays. The next line contains n integers representing the first array . The third line contains n integers representing the second array .

Output

The program should print Yes in case it’s possible to swap two elements to make the arrays equal and No otherwise.

Examples

Input
Output
5 1 2 3 4 5 1 4 3 2 5
Yes
5 1 2 3 4 5 5 6 7 8 9
No
4 1 2 2 4 1 3 3 4
Yes
3 5 7 1 5 7 1
Yes
 
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