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;
int A[200000];

bool check(int n) {
  map<int, int> D;
  int prev = 0;
  for(int i = 0; i < N; ++i) {
    if(A[i] <= prev) {
      D.erase(D.lower_bound(A[i]), D.end());
      int x = A[i] - 1;
      while(true) {
        if(x < 0) return false;
        ++D[x];
        if(D[x] >= n) {
          D.erase(x); --x;
        } else {
          break;
        }
      }
    }
    prev = A[i];
  }
  return true;
}

bool inc() {
  int prev = 0;
  for(int i = 0; i < N; ++i) {
    if(A[i] <= prev) return false;
    prev = A[i];
  }
  return true;
}

int main() {
  cin >> N;
  for(int i = 0; i < N; ++i) cin >> A[i];
  if(inc()) {
    cout << 1 << endl; return 0;
  }
  int ng = 1, ok = N;
  while(ok - ng > 1) {
    int mid = (ng + ok) / 2;
    if(check(mid)) ok = mid;
    else ng = mid;
  }
  cout << ok << endl;
  return 0;
}
