#include <bits/stdc++.h>
const long long N = 2e5 + 1000;
long long n;
long long a[N];
void init() {
  std::cin >> n;
  for (long long i = 1; i <= n; i++) {
    scanf("%I64d", &a[i]);
  }
}
void work() {
  std::map<long long, long long> f;
  f[a[1] - 1] = 0;
  for (long long i = 1; i < n; i++) {
    std::map<long long, long long> tmp;
    std::vector<std::map<long long, long long>::iterator> buffer;
    for (auto it = f.lower_bound(a[i + 1] - 1); it != f.end(); it++) {
      buffer.push_back(it);
      tmp[it->first] = it->second;
    }
    for (auto u : buffer) {
      f.erase(u);
    }
    for (auto u : tmp) {
      f[a[i + 1] - 1] =
          std::max(f[a[i + 1] - 1],
                   u.second + i * (u.first - u.first % a[i + 1] - a[i + 1]));
      f[u.first % a[i + 1]] = std::max(
          f[u.first % a[i + 1]], u.second + i * (u.first - u.first % a[i + 1]));
    }
  }
  long long answer = -1;
  for (auto u : f) {
    answer = std::max(answer, u.second + u.first * n);
  }
  std::cout << answer << std::endl;
}
int main() {
  init();
  work();
  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>
const long long N = 2e5 + 1000;
long long n;
long long a[N];
void init() {
  std::cin >> n;
  for (long long i = 1; i <= n; i++) {
    scanf("%I64d", &a[i]);
  }
}
void work() {
  std::map<long long, long long> f;
  f[a[1] - 1] = 0;
  for (long long i = 1; i < n; i++) {
    std::map<long long, long long> tmp;
    std::vector<std::map<long long, long long>::iterator> buffer;
    for (auto it = f.lower_bound(a[i + 1] - 1); it != f.end(); it++) {
      buffer.push_back(it);
      tmp[it->first] = it->second;
    }
    for (auto u : buffer) {
      f.erase(u);
    }
    for (auto u : tmp) {
      f[a[i + 1] - 1] =
          std::max(f[a[i + 1] - 1],
                   u.second + i * (u.first - u.first % a[i + 1] - a[i + 1]));
      f[u.first % a[i + 1]] = std::max(
          f[u.first % a[i + 1]], u.second + i * (u.first - u.first % a[i + 1]));
    }
  }
  long long answer = -1;
  for (auto u : f) {
    answer = std::max(answer, u.second + u.first * n);
  }
  std::cout << answer << std::endl;
}
int main() {
  init();
  work();
  return 0;
}

```