Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Dima and Staircase

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputDima's got a staircase that consists of *n* stairs. The first stair is at height *a*_{1}, the second one is at *a*_{2}, the last one is at *a*_{n} (1 ≤ *a*_{1} ≤ *a*_{2} ≤ ... ≤ *a*_{n}).

Dima decided to play with the staircase, so he is throwing rectangular boxes at the staircase from above. The *i*-th box has width *w*_{i} and height *h*_{i}. Dima throws each box vertically down on the first *w*_{i} stairs of the staircase, that is, the box covers stairs with numbers 1, 2, ..., *w*_{i}. Each thrown box flies vertically down until at least one of the two following events happen:

- the bottom of the box touches the top of a stair;
- the bottom of the box touches the top of a box, thrown earlier.

We only consider touching of the horizontal sides of stairs and boxes, at that touching with the corners isn't taken into consideration. Specifically, that implies that a box with width *w*_{i} cannot touch the stair number *w*_{i} + 1.

You are given the description of the staircase and the sequence in which Dima threw the boxes at it. For each box, determine how high the bottom of the box after landing will be. Consider a box to fall after the previous one lands.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{5}) — the number of stairs in the staircase. The second line contains a non-decreasing sequence, consisting of *n* integers, *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{9}; *a*_{i} ≤ *a*_{i + 1}).

The next line contains integer *m* (1 ≤ *m* ≤ 10^{5}) — the number of boxes. Each of the following *m* lines contains a pair of integers *w*_{i}, *h*_{i} (1 ≤ *w*_{i} ≤ *n*; 1 ≤ *h*_{i} ≤ 10^{9}) — the size of the *i*-th thrown box.

The numbers in the lines are separated by spaces.

Output

Print *m* integers — for each box the height, where the bottom of the box will be after landing. Print the answers for the boxes in the order, in which the boxes are given in the input.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

5

1 2 3 6 6

4

1 1

3 1

1 1

4 3

Output

1

3

4

6

Input

3

1 2 3

2

1 1

3 1

Output

1

3

Input

1

1

5

1 2

1 10

1 10

1 10

1 10

Output

1

3

13

23

33

Note

The first sample are shown on the picture.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/25/2017 21:28:09 (c2).

Desktop version, switch to mobile version.
User lists

Name |
---|