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)

前綴和

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轉(zhuǎn)載于:https://www.cnblogs.com/sakumia/p/6507119.html

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