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;
#define rep(i,n) for(int i=0;i<int(n);++i)
#define rep1(i,n) for(int i=1;i<=int(n);++i)

int n;
vector<int> a;

int check(int m){
    map<int,int> mp;
    rep1(i,n-1){
        if(a[i-1] < a[i]) continue;
        if(m == 1) return false;
        int pos = a[i];
        mp.erase(mp.upper_bound(pos), mp.end());
        while(true){
            if(mp[pos] < m - 1){
                mp[pos]++;
                mp.erase(mp.upper_bound(pos), mp.end());
                break;
            }
            pos--;
            if(pos == 0) return false;
        }
    }
    return true;
}

int main(void){
    cin >> n;
    a.resize(n);
    rep(i,n) cin >> a[i];
    int l = 0, r = n;
    while(l+1 < r){
        int m = (l+r)/2;
        if(check(m)){
            r = m;
        }else{
            l = m;
        }
    }
    cout << r << endl;
    return 0;
}
