Eming cup Problem D. Game of numbers

Posted 2020-09-02

Time Limit: 0.5 seconds

Memory Limit: 512 mebibytes

Mingming loves playing with numbers, and today, someone gives him a permutation of nn : P_1, P_2\\ldots P_nP?1??,P?2??…P?n??.

Nannan is Mingming‘s friend, then he asked Mingming: if he select a number xx between [l, r][l,r], and them select another number yy in range (x, r](x,r], then calculate A_xA_yA?x??A?y??. It is clear that there are many valid selections. Nannan wants to know the sum of them. As the number can be very large, you only have to output the answer module 10^9 + 710?9??+7

To make Mingming enjoy the game more, Nannan gives him QQ pairs of l, rl,r. Of course, Mingming can solve this problem. But now, he wants to check if you can solve the problem.

More exactly, your task is to calculate \\sum_{l\\le i\\le r}\\sum_{i< j\\le r} A_iA_j∑?l≤i≤r??∑?i<j≤r??A?i??A?j?? module 10^9 + 710?9??+7 for each l, rl,r, where A_1, A_2, \\ldots A_nA?1??,A?2??,…A?n?? is a permutation of nn.

Input

First line is a number nn(3\\le n\\le 10^53≤n≤10?5??), which means the length of sequence a.

Second line is nn numbers from A_1A?1?? to A_nA?n??(1\\le A_i\\le 10^51≤A?i??≤10?5??, for each i \\neq ji≠j, A_i \\neq A_jA?i??≠A?j??).

Third line is a number Q(1\\le Q\\le 10^5)Q(1≤Q≤10?5??) means how many pairs of ll and rr will be chosen.

In the next QQ lines, the ii-th one contians two integers ll and rr (l< rl<r), which is the ii-th query.

Output

Output QQ lines of answers for each pairs query.

Examples

Sample Input

5
3 2 4 1 5
2
1 2
2 4

Sample Output

6
14

Note

2 times× 500000004 \\equiv≡ 1 (mod 10^9+710?9??+7)

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