Mod Mod Mod
Description
You are given a sequence of integers a1, a2, ..., an. Let 
, and 
for 1 ≤ i < n. Here, 
denotes the modulus operation. Find the maximum value of f(x, 1) over all nonnegative integers x.
The first line contains a single integer n (1 ≤ n ≤ 200000) — the length of the sequence.
The second lines contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1013) — the elements of the sequence.
Output a single integer — the maximum value of f(x, 1) over all nonnegative integers x.
Input
The first line contains a single integer n (1 ≤ n ≤ 200000) — the length of the sequence.
The second lines contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1013) — the elements of the sequence.
Output
Output a single integer — the maximum value of f(x, 1) over all nonnegative integers x.
Samples
2
10 5
13
5
5 4 3 2 1
6
4
5 10 5 10
16
Note
In the first example you can choose, for example, x = 19.
In the second example you can choose, for example, x = 3 or x = 2.