You are given a sequence A of N (N≤250000) integers between 1 and 50000. On this sequence you have to apply M (M≤10000) operations of the form: modify the i-th element in the sequence and then say how many inversions are there in the sequence. The number of inversions in a sequence is given by the number of pairs (i,j) with i < j and Ai > Aj.

Input

The first line of input contains the number N and the next line contains the numbers that form the sequence. After that follows the number M and then M lines, each containig 2 integers X and Y, meaning that new value of the X-th element of the sequence is Y and that you should count the number of inversions in the modified sequence.

Output

Output must contain M lines, the i-th line of output containg the number of inversions in the sequence after the first i operations.

Example

Input:
10
2 6 6 4 7 6 3 5 9 1 
7
8 8
5 1
5 6
10 5
7 1
10 10
4 6

Output:
17
18
16
13
14
8
6