#include <bits/stdc++.h>
std::map<long long, long long> map;
int n;
long long a;
void update(long long r, long long k) {
  r = -r;
  if (map.count(r))
    map[r] = std::max(map[r], k);
  else
    map[r] = k;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &a);
    if (i == 1) update(a - 1, 0);
    for (auto it = map.begin(), tem = it; it != map.end();) {
      long long f = -it->first, s = it->second;
      if (f < a) break;
      update(a - 1, s + (1ll * (i - 1) * (f - (f % a) - a)));
      update((f % a), s + (1ll * (i - 1) * (f - (f % a))));
      tem = it;
      ++it;
      map.erase(tem);
    }
  }
  long long ans = 0;
  for (auto it = map.begin(); it != map.end(); ++it)
    ans = std::max(ans, 1ll * n * (-it->first) + it->second);
  printf("%I64d", ans);
}

### Prompt

Please create a solution in cpp to the following problem:

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>
std::map<long long, long long> map;
int n;
long long a;
void update(long long r, long long k) {
  r = -r;
  if (map.count(r))
    map[r] = std::max(map[r], k);
  else
    map[r] = k;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &a);
    if (i == 1) update(a - 1, 0);
    for (auto it = map.begin(), tem = it; it != map.end();) {
      long long f = -it->first, s = it->second;
      if (f < a) break;
      update(a - 1, s + (1ll * (i - 1) * (f - (f % a) - a)));
      update((f % a), s + (1ll * (i - 1) * (f - (f % a))));
      tem = it;
      ++it;
      map.erase(tem);
    }
  }
  long long ans = 0;
  for (auto it = map.begin(); it != map.end(); ++it)
    ans = std::max(ans, 1ll * n * (-it->first) + it->second);
  printf("%I64d", ans);
}

```