#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 111;
int N;
long long A[maxn];
map<long long, long long> f;
void rl(long long &x) {
  char ch = (getchar());
  x = 0;
  while ((ch < '0' || ch > '9')) ch = (getchar());
  while (!(ch < '0' || ch > '9')) x = x * 10 + ch - '0', ch = (getchar());
}
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; ++i) rl(A[i]);
  f[A[1] - 1] = 0;
  for (int i = 2; i <= N; ++i)
    for (map<long long, long long>::iterator j = f.lower_bound(A[i]);
         j != f.end(); f.erase(j++)) {
      long long x = j->first, y = j->second;
      f[x % A[i]] = max(f[x % A[i]], y + 1ll * (i - 1) * (x - x % A[i]));
      f[A[i] - 1] =
          max(f[A[i] - 1], y + 1ll * (i - 1) * ((x + 1) / A[i] * A[i] - A[i]));
    }
  long long ans = 0;
  for (map<long long, long long>::iterator i = f.begin(); i != f.end(); ++i)
    ans = max(ans, i->first * N + i->second);
  cout << ans;
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
const int maxn = 2e5 + 111;
int N;
long long A[maxn];
map<long long, long long> f;
void rl(long long &x) {
  char ch = (getchar());
  x = 0;
  while ((ch < '0' || ch > '9')) ch = (getchar());
  while (!(ch < '0' || ch > '9')) x = x * 10 + ch - '0', ch = (getchar());
}
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; ++i) rl(A[i]);
  f[A[1] - 1] = 0;
  for (int i = 2; i <= N; ++i)
    for (map<long long, long long>::iterator j = f.lower_bound(A[i]);
         j != f.end(); f.erase(j++)) {
      long long x = j->first, y = j->second;
      f[x % A[i]] = max(f[x % A[i]], y + 1ll * (i - 1) * (x - x % A[i]));
      f[A[i] - 1] =
          max(f[A[i] - 1], y + 1ll * (i - 1) * ((x + 1) / A[i] * A[i] - A[i]));
    }
  long long ans = 0;
  for (map<long long, long long>::iterator i = f.begin(); i != f.end(); ++i)
    ans = max(ans, i->first * N + i->second);
  cout << ans;
  return 0;
}

```