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;
using PP = pair<long, long>;
const int INF = 1e9;
template <class T> T Next() { T buf; cin >> buf; return buf; }

int n;
int a[200000];

bool ok(int kind) {
  map<int, int> mp;
  for (int i = 1; i < n; ++i) {
    if (a[i - 1] < a[i]) continue;
    if (kind == 1) return false;
    
    int idx = a[i];
    while (idx > 0 && mp[idx] == kind - 1) {
      mp[idx] = 0;
      --idx;
    }
    if (idx == 0) return false;
    ++mp[idx];
    
    mp.erase(mp.upper_bound(idx), mp.end());
  }
  return true;
}

int sub() {
  int lo = 0;
  int hi = 200001;
  while (hi - lo > 1) {
    int mid = (lo + hi) / 2;
    if (ok(mid)) {
      hi = mid;
    } else {
      lo = mid;
    }
  }
  return hi;
}

int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  
  cout << sub() << endl;
}