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 <algorithm>
#include <cstdio>
#include <vector>

const int N = 200050;

int n, A[N];
std::vector<std::pair<int, int> > K;

bool check(int d) {
  K.clear();
  K.push_back(std::make_pair(0, 0));
  for (int i = 1; i <= n; ++i)
    if (A[i] <= A[i - 1]) {
      while (K.back().first > A[i]) K.pop_back();
      for (int j = A[i]; ; --j) {
        if (j < 1) return false;
        int t = 1;
        if (K.back().first == j) t = 1 + K.back().second, K.pop_back();
        if (t < d) {
          K.push_back(std::make_pair(j, t));
          break;
        }
      }
    }
  return true;
}

int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &A[i]);
  int l = 1, r = n;
  while (l < r) {
    int mid = (l + r) / 2;
    if (check(mid)) r = mid;
    else l = mid + 1;
  }
  printf("%d\n", l);
  return 0;
}