G. The Great Equalizer
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Tema bought an old device with a small screen and a worn-out inscription "The Great Equalizer" on the side.

The seller said that the device needs to be given an array $$$a$$$ of integers as input, after which "The Great Equalizer" will work as follows:

  1. Sort the current array in non-decreasing order and remove duplicate elements leaving only one occurrence of each element.
  2. If the current length of the array is equal to $$$1$$$, the device stops working and outputs the single number in the array — output value of the device.
  3. Add an arithmetic progression {$$$n,\ n - 1,\ n - 2,\ \ldots,\ 1$$$} to the current array, where $$$n$$$ is the length of the current array. In other words, $$$n - i$$$ is added to the $$$i$$$-th element of the array, when indexed from zero.
  4. Go to the first step.

To test the operation of the device, Tema came up with a certain array of integers $$$a$$$, and then wanted to perform $$$q$$$ operations on the array $$$a$$$ of the following type:

  1. Assign the value $$$x$$$ ($$$1 \le x \le 10^9$$$) to the element $$$a_i$$$ ($$$1 \le i \le n$$$).
  2. Give the array $$$a$$$ as input to the device and find out the result of the device's operation, while the array $$$a$$$ remains unchanged during the operation of the device.

Help Tema find out the output values of the device after each operation.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Then follows the description of each test case.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the size of the array $$$a$$$ that Tema initially came up with.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, a_3, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the elements of the array $$$a$$$.

The third line of a set contains a single integer $$$q$$$ ($$$1 \le q \le 2 \cdot 10^5$$$) — the number of operations.

Each of the next $$$q$$$ lines of a test case contains two integers $$$i$$$ ($$$1 \le i \le n$$$) and $$$x$$$ ($$$1 \le x \le 10^9$$$) - the descriptions of the operations.

It is guaranteed that the sum of the values of $$$n$$$ and the sum of the values of $$$q$$$ for all test cases do not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output $$$q$$$ integers — the output values of the device after each operation.

Example
Input
4
3
2 4 8
3
1 6
2 10
3 1
5
1 2 2 2 2
1
5 3
2
5 6
7
1 2
1 7
1 7
2 5
1 2
2 7
2 2
5
2 5 1 10 6
10
1 7
4 8
2 5
1 4
2 8
3 4
1 9
3 7
3 4
3 1
Output
10 12 15 
4 
10 8 8 9 8 12 2 
14 12 12 11 11 10 11 10 11 14
Note

Let's consider the first example of the input.

Initially, the array of numbers given as input to the device will be $$$[6, 4, 8]$$$. It will change as follows: $$$$$$[6, 4, 8] \rightarrow [4, 6, 8] \rightarrow [7, 8, 9] \rightarrow [10, 10, 10] \rightarrow [10]$$$$$$

Then, the array of numbers given as input to the device will be $$$[6, 10, 8]$$$. It will change as follows: $$$$$$[6, 10, 8] \rightarrow [6, 8, 10] \rightarrow [9, 10, 11] \rightarrow [12, 12, 12] \rightarrow [12]$$$$$$

The last array of numbers given as input to the device will be $$$[6, 10, 1]$$$. It will change as follows: $$$$$$[6, 10, 1] \rightarrow [1, 6, 10] \rightarrow [4, 8, 11] \rightarrow [7, 10, 12] \rightarrow [10, 12, 13] \rightarrow [13, 14, 14] \rightarrow [13, 14] \rightarrow [15, 15] \rightarrow [15]$$$$$$