Faster range queries

Given an array a of n integers, you are asked to answer q queries. All the queries have the form: β€œWhat is the sum of elements in the array a between indices [l; r]?” (both endpoints are inclusive and the indexing starts from 0). This time the number of queries and the size of the array are significantly larger. Can you think of a way to answer those queries faster?

Input

The first line of the input contains a single integer n - the number of elements in the array (1 ≀ n ≀ ). The next line contains n integers separated by a space, that represent the elements of the array .
The following line contains a single integer q - the number of queries (1 ≀ q ≀ ). The next q lines contain queries of the form .

Output

The program should print q lines, each of which is the sum of elements in the array a between indices (both inclusive).

Examples

Input
Output
8 1 2 3 4 5 6 7 8 3 0 4 5 6 5 7
15 13 21

Constraints

Time limit: 4 seconds

Memory limit: 512 MB

Output limit: 25 MB

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