#include <bits/stdc++.h>
using namespace std;
long long n, a[200001], f[200001], j;
int main() {
  scanf("%I64d", &n);
  for (long long i = n; i; i--)
    scanf("%I64d", &a[i]), a[i] = i < n ? min(a[i], a[i + 1]) : a[i];
  a[0] = 1;
  for (long long i = 1; i <= n; i++)
    for (long long k = a[i], l = 0; k; k %= a[j]) {
      j = lower_bound(a + 1, a + n + 1, k) - a - 1;
      f[i] = max(f[i], f[j] + (n - j) * (k / a[j] - 1) * a[j] + l);
      l += (n - j) * (k / a[j]) * a[j];
    }
  printf("%I64d\n", f[n]);
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

You are given a sequence of integers a1, a2, ..., an. Let <image>, and <image> for 1 ≤ i < n. Here, <image> denotes the modulus operation. Find 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.

Examples

Input

2
10 5


Output

13


Input

5
5 4 3 2 1


Output

6


Input

4
5 10 5 10


Output

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long n, a[200001], f[200001], j;
int main() {
  scanf("%I64d", &n);
  for (long long i = n; i; i--)
    scanf("%I64d", &a[i]), a[i] = i < n ? min(a[i], a[i + 1]) : a[i];
  a[0] = 1;
  for (long long i = 1; i <= n; i++)
    for (long long k = a[i], l = 0; k; k %= a[j]) {
      j = lower_bound(a + 1, a + n + 1, k) - a - 1;
      f[i] = max(f[i], f[j] + (n - j) * (k / a[j] - 1) * a[j] + l);
      l += (n - j) * (k / a[j]) * a[j];
    }
  printf("%I64d\n", f[n]);
  return 0;
}

```