#include <bits/stdc++.h>
using namespace std;
map<long long, long long> f;
map<long long, long long>::iterator it;
long long a, b, v, ans;
int n;
inline long long gi() {
  register long long x = 0, q = 1;
  register char ch = getchar();
  while ((ch < '0' || ch > '9') && ch != '-') ch = getchar();
  if (ch == '-') q = -1, ch = getchar();
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  return q * x;
}
int main() {
  n = gi(), f[gi() - 1] = 0;
  for (register int i = 2; i <= n; ++i) {
    v = gi();
    while (f.begin() != f.end()) {
      it = f.end(), a = (*(--it)).first;
      b = (*it).second;
      if (a < v) break;
      f[v - 1] = max(f[v - 1], f[a] + (a - a % v - v) * (i - 1));
      f[a % v] = max(f[a % v], f[a] + (a - a % v) * (i - 1)), f.erase(it);
    }
  }
  for (it = f.begin(); it != f.end(); ++it)
    ans = max(ans, (*it).first * n + (*it).second);
  cout << ans;
  return 0;
}

### Prompt

Please formulate a CPP solution 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>
using namespace std;
map<long long, long long> f;
map<long long, long long>::iterator it;
long long a, b, v, ans;
int n;
inline long long gi() {
  register long long x = 0, q = 1;
  register char ch = getchar();
  while ((ch < '0' || ch > '9') && ch != '-') ch = getchar();
  if (ch == '-') q = -1, ch = getchar();
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  return q * x;
}
int main() {
  n = gi(), f[gi() - 1] = 0;
  for (register int i = 2; i <= n; ++i) {
    v = gi();
    while (f.begin() != f.end()) {
      it = f.end(), a = (*(--it)).first;
      b = (*it).second;
      if (a < v) break;
      f[v - 1] = max(f[v - 1], f[a] + (a - a % v - v) * (i - 1));
      f[a % v] = max(f[a % v], f[a] + (a - a % v) * (i - 1)), f.erase(it);
    }
  }
  for (it = f.begin(); it != f.end(); ++it)
    ans = max(ans, (*it).first * n + (*it).second);
  cout << ans;
  return 0;
}

```