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;

bool can(int n, const vector<int> &a, int x) {
  if (x == 1)
    for (int i = 1; i < n; ++i)
      if (a[i] <= a[i - 1])
        return false;
  map<int, int> ma;
  for (int i = 1; i < n; ++i) {
    if (a[i] > a[i - 1])
      continue;
    int k = a[i];
    auto p = ma.upper_bound(k);
    if (p != ma.end())
      ma.erase(p);
    ++ma[k];
    while (k > 0 && ma[k] == x) {
      ma.erase(k);
      ++ma[--k];
    }
    if (k == 0)
      return false;
  }
  return true;
}

int main() {
  int n;
  scanf("%d", &n);
  vector<int> a(n);
  for (int i = 0; i < n; ++i)
    scanf("%d", &a[i]);
  int low = 0, high = n + 1;
  while (low + 1 < high) {
    int mid = (low + high) / 2;
    (can(n, a, mid) ? high : low) = mid;
  }
  printf("%d\n", high);
  return 0;
}