문제

Little Daniel has a bag of candy and N cards. Each of the cards has a positive integer $P_{i}$ written on it. While Daniel was eating his candy, he thought of a fun game. He can tie together two cards with labels a and b, and then he must eat min($P_{a}$% $P_{b}$, $P_{b}$% $P_{a}$) of candy, where operation x% y denotes the remainder when dividing x with y. He wants to tie together pairs of cards in a way that, when he lifts one of them, all the rest are also lifted up. Each card can be directly connected with a tie to any number of other cards. As Daniel is watching his figure, he doesn’t want to consume too much, so he is asking you to calculate the minimal number of candy he must eat so all cards are connected.

입력

The first line of input contains the positive integer N. (1 ≤ N ≤ $10^{5}$) Each of the following N lines contains a positive integer $P_{i}$ (1 ≤ $P_{i}$ ≤ $10^{7}$).

출력

The first and only line of output must contain the required value from the task.

채점

In test cases worth 30% of total points, it will hold N ≤ $10^{3}$. In test cases worth 40% of total points, it will hold $P_{i}$ ≤ $10^{6}$. In test cases worth 70% of total points, at least one of the two conditions will hold.

예제 입력 1

4
2
6
3
11

예제 출력 1

1

예제 입력 2

4
1
2
3
4

예제 출력 2

0

예제 입력 3

3
4
9
15

예제 출력 3

4