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<iostream>
#include<vector>
#include<algorithm>
#include<map>

using namespace std;

vector<long long> a;

bool check(int k){
    map<int, int> mp;
    for(int i = 1; i < a.size(); i++){
        if(a[i] > a[i - 1]) continue;
        if(k == 1) return false;
        if(a[i] <= a[i - 1]){
            int p = a[i];
            mp.erase(mp.upper_bound(p), mp.end());
            while(mp[p] == k - 1){
                p--;
                if(p == 0) return false;
            }
            mp[p]++;
            mp.erase(mp.upper_bound(p), mp.end());
        }
    }
    return true;
}

int main(){
    int n;
    cin >> n;
    a.resize(n);
    for(int i = 0; i < n; i++){
        cin >> a[i];
    }
    int l = 0, r = 200010;
    while(r - l > 1){
        int mid = (l + r) / 2;
        if(check(mid))
            r = mid;
        else
            l = mid; 
    }
    cout << r << endl;
    return 0;
}
