Story

Koboshi-san is solving competitive programming problems. One problem stated the following:

Since the answer can be very large, print the remainder when $10^9+7$ is divided by the answer.

Koboshi-san misread this as "print the remainder when the answer is divided by $10^9+7$", and so could not solve it.

Feeling sad, Koboshi-san decided to investigate the error between the correct output and Koboshi-san's output. When the answer is $X$ and the divisor is $Y$, this error is expressed as $|(X\bmod{Y})-(Y\bmod{X})|$.

Based on this, Koboshi-san created the following problem.

Problem Statement

Given pairwise distinct positive integers $A_1,A_2,\ldots,A_N$, find the value of

.

Here, $a\bmod{b}$ denotes the remainder when $a$ is divided by $b$.

Pay attention to the execution time limit.

Constraints

• $2\le N\le 2\times 10^5$
• $1\le A_i\le 2\times 10^5$
• If $i\ne j$, then $A_i\ne A_j$
• All inputs are integers

Input

$N$
$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print the answer.

Sample

2
3 5

1

3
1 11 111

12

9
1 9 2 8 3 7 4 6 5

83