#include <bits/stdc++.h>
using ll = long long;
int const nmax = 200000;
ll v[5 + nmax];
std::map<ll, ll> mp;
void _insert(ll x, ll y) { mp[x] = std::max(mp[x], y); }
int main() {
  std::ios::sync_with_stdio(0);
  std::cin.tie(0);
  int n;
  std::cin >> n;
  for (int i = 1; i <= n; i++) std::cin >> v[i];
  mp[v[1] - 1] = 0;
  v[n + 1] = 1;
  for (int i = 1; i <= n; i++) {
    std::vector<std::pair<ll, ll>> sol2;
    while (0 < mp.size()) {
      std::map<ll, ll>::iterator it = mp.end();
      it--;
      if (v[i + 1] <= it->first) {
        ll last = it->first - it->first % v[i + 1];
        sol2.push_back({it->first % v[i + 1], last * i + it->second});
        if (0 <= (last - v[i + 1]))
          sol2.push_back({v[i + 1] - 1, (last - v[i + 1]) * i + it->second});
        _insert(it->first % v[i + 1], last * i + it->second);
        _insert(v[i + 1] - 1, (last - v[i + 1]) * i + it->second);
        mp.erase(it);
      } else
        break;
    }
  }
  std::cout << mp[0];
  return 0;
}

### Prompt

Please create a solution in cpp 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 ll = long long;
int const nmax = 200000;
ll v[5 + nmax];
std::map<ll, ll> mp;
void _insert(ll x, ll y) { mp[x] = std::max(mp[x], y); }
int main() {
  std::ios::sync_with_stdio(0);
  std::cin.tie(0);
  int n;
  std::cin >> n;
  for (int i = 1; i <= n; i++) std::cin >> v[i];
  mp[v[1] - 1] = 0;
  v[n + 1] = 1;
  for (int i = 1; i <= n; i++) {
    std::vector<std::pair<ll, ll>> sol2;
    while (0 < mp.size()) {
      std::map<ll, ll>::iterator it = mp.end();
      it--;
      if (v[i + 1] <= it->first) {
        ll last = it->first - it->first % v[i + 1];
        sol2.push_back({it->first % v[i + 1], last * i + it->second});
        if (0 <= (last - v[i + 1]))
          sol2.push_back({v[i + 1] - 1, (last - v[i + 1]) * i + it->second});
        _insert(it->first % v[i + 1], last * i + it->second);
        _insert(v[i + 1] - 1, (last - v[i + 1]) * i + it->second);
        mp.erase(it);
      } else
        break;
    }
  }
  std::cout << mp[0];
  return 0;
}

```