#include <bits/stdc++.h>
using namespace std;
const int MAXN = 500005;
const int INF = 0x3f3f3f3f;
template <typename T>
inline void read(T &AKNOI) {
  T x = 0, flag = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') flag = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  AKNOI = flag * x;
}
template <typename T>
inline void cmax(T &x, T y) {
  if (x < y) x = y;
}
int n;
map<long long, long long> dp;
map<long long, long long>::iterator it;
void solve() {
  read(n);
  long long a;
  read(a);
  dp[a - 1] = 0;
  for (int i = 2; i <= n; ++i) {
    read(a);
    while (dp.size()) {
      it = --dp.end();
      long long r = it->first, p = it->second;
      if (r < a) break;
      cmax(dp[a - 1], p + (r - r % a - a) * (i - 1));
      cmax(dp[r % a], p + (r - r % a) * (i - 1));
      dp.erase(it);
    }
  }
  long long ans = 0;
  for (auto p : dp) {
    cmax(ans, p.first * n + p.second);
  }
  printf("%lld\n", ans);
}
int main() {
  solve();
  return 0;
}

### Prompt

Your task is to create a Cpp solution 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 MAXN = 500005;
const int INF = 0x3f3f3f3f;
template <typename T>
inline void read(T &AKNOI) {
  T x = 0, flag = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') flag = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  AKNOI = flag * x;
}
template <typename T>
inline void cmax(T &x, T y) {
  if (x < y) x = y;
}
int n;
map<long long, long long> dp;
map<long long, long long>::iterator it;
void solve() {
  read(n);
  long long a;
  read(a);
  dp[a - 1] = 0;
  for (int i = 2; i <= n; ++i) {
    read(a);
    while (dp.size()) {
      it = --dp.end();
      long long r = it->first, p = it->second;
      if (r < a) break;
      cmax(dp[a - 1], p + (r - r % a - a) * (i - 1));
      cmax(dp[r % a], p + (r - r % a) * (i - 1));
      dp.erase(it);
    }
  }
  long long ans = 0;
  for (auto p : dp) {
    cmax(ans, p.first * n + p.second);
  }
  printf("%lld\n", ans);
}
int main() {
  solve();
  return 0;
}

```