#include <bits/stdc++.h>
using namespace std;
const int MAXN = 200005;
int n;
long long a[MAXN];
map<long long, long long> f;
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    (x *= 10) += ch - '0';
    ch = getchar();
  }
  return x * f;
}
int main() {
  n = read();
  for (int i = 1; i <= n; i++) a[i] = read();
  f[a[1] - 1] = 0;
  long long x, y;
  for (int i = 1; i < n; i++)
    for (auto j = f.lower_bound(a[i + 1]); j != f.end(); f.erase(j++)) {
      x = j->first, y = j->second;
      f[x % a[i + 1]] = max(f[x % a[i + 1]], y + i * (x - x % a[i + 1]));
      f[a[i + 1] - 1] =
          max(f[a[i + 1] - 1], y + i * (x / a[i + 1] * a[i + 1] - a[i + 1]));
    }
  long long ans = 0;
  for (auto j = f.begin(); j != f.end(); j++)
    ans = max(ans, n * j->first + j->second);
  printf("%lld\n", 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 = 200005;
int n;
long long a[MAXN];
map<long long, long long> f;
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    (x *= 10) += ch - '0';
    ch = getchar();
  }
  return x * f;
}
int main() {
  n = read();
  for (int i = 1; i <= n; i++) a[i] = read();
  f[a[1] - 1] = 0;
  long long x, y;
  for (int i = 1; i < n; i++)
    for (auto j = f.lower_bound(a[i + 1]); j != f.end(); f.erase(j++)) {
      x = j->first, y = j->second;
      f[x % a[i + 1]] = max(f[x % a[i + 1]], y + i * (x - x % a[i + 1]));
      f[a[i + 1] - 1] =
          max(f[a[i + 1] - 1], y + i * (x / a[i + 1] * a[i + 1] - a[i + 1]));
    }
  long long ans = 0;
  for (auto j = f.begin(); j != f.end(); j++)
    ans = max(ans, n * j->first + j->second);
  printf("%lld\n", ans);
  return 0;
}

```