#include <bits/stdc++.h>
using namespace std;
bool home = 1;
signed realMain();
signed main() {
  home = 0;
  if (home) {
    freopen("tony_stark", "r", stdin);
  } else {
    ios::sync_with_stdio(0);
    cin.tie(0);
  }
  realMain();
}
const long long N = 200000 + 7;
long long n, a[N];
map<long long, long long> memo;
void rec(long long a, long long relax) { memo[a] = max(memo[a], relax); }
long long getdp(long long i, long long x) {
  long long ret = 0;
  for (auto &it : memo) {
    if (x <= it.first) {
      ret = max(ret, i * x + it.second);
    }
  }
  return ret;
}
signed realMain() {
  cin >> n;
  for (long long i = 1; i <= n; i++) {
    cin >> a[i];
  }
  a[n + 1] = 1;
  memo[a[1] - 1] = 0;
  for (long long i = 2; i <= n + 1; i++) {
    long long mod = a[i];
    while (1) {
      auto it = memo.end();
      it--;
      if (it->first < mod) {
        break;
      }
      long long pre = it->first, add = it->second;
      memo.erase(it);
      rec(pre % mod, add + (pre / mod) * mod * (i - 1));
      if (pre % mod != mod - 1) {
        pre = pre - pre % mod - 1;
      }
      rec(pre % mod, add + (pre / mod) * mod * (i - 1));
    }
  }
  cout << memo[0] << "\n";
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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;
bool home = 1;
signed realMain();
signed main() {
  home = 0;
  if (home) {
    freopen("tony_stark", "r", stdin);
  } else {
    ios::sync_with_stdio(0);
    cin.tie(0);
  }
  realMain();
}
const long long N = 200000 + 7;
long long n, a[N];
map<long long, long long> memo;
void rec(long long a, long long relax) { memo[a] = max(memo[a], relax); }
long long getdp(long long i, long long x) {
  long long ret = 0;
  for (auto &it : memo) {
    if (x <= it.first) {
      ret = max(ret, i * x + it.second);
    }
  }
  return ret;
}
signed realMain() {
  cin >> n;
  for (long long i = 1; i <= n; i++) {
    cin >> a[i];
  }
  a[n + 1] = 1;
  memo[a[1] - 1] = 0;
  for (long long i = 2; i <= n + 1; i++) {
    long long mod = a[i];
    while (1) {
      auto it = memo.end();
      it--;
      if (it->first < mod) {
        break;
      }
      long long pre = it->first, add = it->second;
      memo.erase(it);
      rec(pre % mod, add + (pre / mod) * mod * (i - 1));
      if (pre % mod != mod - 1) {
        pre = pre - pre % mod - 1;
      }
      rec(pre % mod, add + (pre / mod) * mod * (i - 1));
    }
  }
  cout << memo[0] << "\n";
  return 0;
}

```