Bubble Sort

Write a program of the Bubble Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:

BubbleSort(A) 1 for i = 0 to A.length-1 2 for j = A.length-1 downto i+1 3 if A[j] < A[j-1] 4 swap A[j] and A[j-1]

Note that, indices for array elements are based on 0-origin.

Your program should also print the number of swap operations defined in line 4 of the pseudocode.

Constraints

1 ≤ N ≤ 100

Input

The first line of the input includes an integer N, the number of elements in the sequence.

In the second line, N elements of the sequence are given separated by spaces characters.

Output

The output consists of 2 lines.

In the first line, please print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.

In the second line, please print the number of swap operations.

Examples

Input

5 5 3 2 4 1

Output

1 2 3 4 5 8

Input

6 5 2 4 6 1 3

Output

1 2 3 4 5 6 9

inputFormat

Input

The first line of the input includes an integer N, the number of elements in the sequence.

In the second line, N elements of the sequence are given separated by spaces characters.

outputFormat

Output

The output consists of 2 lines.

In the first line, please print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.

In the second line, please print the number of swap operations.

Examples

Input

5 5 3 2 4 1

Output

1 2 3 4 5 8

Input

6 5 2 4 6 1 3

Output

1 2 3 4 5 6 9

样例

5
5 3 2 4 1

1 2 3 4 5
8

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