#include <bits/stdc++.h>
using namespace std;
const int N = 200010;
set<pair<long long, long long> > S;
vector<pair<long long, long long> > g;
int k, n, m, l;
long long Ans;
long long x, lst;
int main() {
  scanf("%d%I64d", &n, &lst);
  S.insert(pair<long long, long long>(lst - 1, 0));
  for (int i = 1; i < n; i++) {
    scanf("%I64d", &x);
    if (x >= lst) continue;
    lst = x;
    g.clear();
    while (!S.empty()) {
      set<pair<long long, long long> >::iterator I = S.end();
      I--;
      if ((*I).first < x) break;
      g.push_back((*I));
      S.erase(I);
    }
    if (!(g.size())) continue;
    long long mx = 0;
    for (int j = 0; j < g.size(); j++) {
      pair<long long, long long> t = g[j];
      mx = max(mx, t.second + 1ll * i * (t.first - x - t.first % x));
      S.insert(pair<long long, long long>(
          t.first % x, t.second + 1ll * i * (t.first - t.first % x)));
    }
    S.insert(pair<long long, long long>(x - 1, mx));
  }
  for (set<pair<long long, long long> >::iterator I = S.begin(); I != S.end();
       I++) {
    pair<long long, long long> t = (*I);
    Ans = max(Ans, n * t.first + t.second);
  }
  cout << Ans << endl;
  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 namespace std;
const int N = 200010;
set<pair<long long, long long> > S;
vector<pair<long long, long long> > g;
int k, n, m, l;
long long Ans;
long long x, lst;
int main() {
  scanf("%d%I64d", &n, &lst);
  S.insert(pair<long long, long long>(lst - 1, 0));
  for (int i = 1; i < n; i++) {
    scanf("%I64d", &x);
    if (x >= lst) continue;
    lst = x;
    g.clear();
    while (!S.empty()) {
      set<pair<long long, long long> >::iterator I = S.end();
      I--;
      if ((*I).first < x) break;
      g.push_back((*I));
      S.erase(I);
    }
    if (!(g.size())) continue;
    long long mx = 0;
    for (int j = 0; j < g.size(); j++) {
      pair<long long, long long> t = g[j];
      mx = max(mx, t.second + 1ll * i * (t.first - x - t.first % x));
      S.insert(pair<long long, long long>(
          t.first % x, t.second + 1ll * i * (t.first - t.first % x)));
    }
    S.insert(pair<long long, long long>(x - 1, mx));
  }
  for (set<pair<long long, long long> >::iterator I = S.begin(); I != S.end();
       I++) {
    pair<long long, long long> t = (*I);
    Ans = max(Ans, n * t.first + t.second);
  }
  cout << Ans << endl;
  return 0;
}

```