There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.

At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the minimum possible number of different characters contained in the strings.

Examples

Input

3
3 2 1


Output

2


Input

5
2 3 2 1 2


Output

2
#include <bits/stdc++.h>
using namespace std;

int n, a[200005];
map<int, int> mp;

bool check(int lmt) {
  mp.clear();
  int now = 0;
  for (int i = 1; i <= n; ++i) {
    if (a[i] > now) now = a[i];
    else {
      now = a[i];
      while (!mp.empty()) {
        int last = (--mp.end())->first;
        if (last >= now) mp.erase(last);
        else break;
      }
      int nnow = now - 1;
      mp[nnow]++;
      while (nnow >= 0 && mp[nnow] >= lmt) {
        mp.erase(nnow);
        --nnow;
        mp[nnow]++;
      }
      if (nnow < 0) return false;
    }
  }
  return true;
}

int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i)
    scanf("%d", a + i);
  bool flag = true;
  for (int i = 1; i <= n; ++i)
    flag &= (a[i] > a[i - 1]);
  if (flag) return puts("1") & 0;
  int l = 2, r = n, ans = n;
  while (l <= r) {
    int mid = l + r >> 1;
    if (check(mid)) ans = mid, r = mid - 1;
    else l = mid + 1;
  }
  printf("%d\n", ans);
  return 0;
}
