You are given an array \(A\) of \(N\) integers. The following two operations can be performed on the provided array and each operation costs 1 unit.

1. Change the value of any element (only one element).
2. Perform cyclic shifts to the array to left by 1 unit. For example, if an array is \(2\ 3\ 1\ 4\) and 1 left shift is performed, then the array becomes \(3\ 1\ 4\ 2\).

You are given \(Q\) queries of type \(X\ B\). For each query, you must replace the value of the element at index \(X\) with \(B\). Find the minimum cost required to convert array \(A\) to the identity array.

An identity array of size \(N\) is \(1,\ 2,\ 3,\ ...,\ N-1,\ N\). 

Note: For each query, you cannot perform actual operations on array \(A\) apart from setting \(A[X]\) to \(B\).

Input format

• The first line contains \(N\) denoting the number of elements in the array.
• The second line contains \(N\) space-separated integers.
• The next line contains \(Q\) denoting the number of queries.
• The next \(Q\) lines contain queries of type \(X\ B\).

Output format
Print \(Q\) integers in a separate line representing the answer to \(Q\) queries.

Constraints
\(1 \le N,\ Q \le 1e5\\ 1 \le X \le N\\ 1 \le A[i],\ B \le 10^9\)