## CBOJ Welcome Contest Problem 4 - Remainder Table

We've all heard of the times table, but what about the remainder table?

Similar to the times table, the remainder table is a table used to define the modulo operator. The cell at \((i, j)\) will be equal to `i % j`

.

Bob wants to test your knowledge on the remainder table! He has given you an array of \(N\) positive integers \(A\). Instead of `i % j`

, he will ask you to get the value of `A[i] % A[j]`

, where \((0 \le i, j \le N - 1)\).

To make the checking process easier for Bob, he will simply ask you to output the sum of all \(N^2\) cells. Can you do it fast enough?

#### Input Specification

The first line of the input will contain an integer \(N\) \((1 \le N \le 10^5)\), indicating the length of the array \(A\).

The next line of the input will contain \(N\) integer ranging from \(1\) to \(10^5\) inclusive, denoting the values of the array \(A\).

#### Output Specification

Output an integer, representing the sum of all \(N^2\) cells in the remainder array.

#### Subtasks

##### Subtask 1 [30%]

\(1 \le N \le 1000\)

All the integers in the array will range from \(1\) to \(10^3\) inclusive.

##### Subtask 2 [30%]

\(1 \le N \le 10^5\)

All the integers in the array will range from \(1\) to \(10^3\) inclusive.

##### Subtask 3 [40%]

No additional constraints.

#### Sample Input

```
4
2 5 5 4
```

#### Sample Output

`18`

#### Sample Explanation

The table of remainder for \([2, 5, 5, 4]\) is as follows:

\(2\) | \(5\) | \(5\) | \(4\) | |
---|---|---|---|---|

\(2\) | \(0\) | \(1\) | \(1\) | \(0\) |

\(5\) | \(2\) | \(0\) | \(0\) | \(4\) |

\(5\) | \(2\) | \(0\) | \(0\) | \(4\) |

\(4\) | \(2\) | \(1\) | \(1\) | \(0\) |

The sum of \(1 + 1 + 2 + 4 + 2 + 4 + 2 + 1 + 1\) is equal to \(18\).

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