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 ll long long

int main(){
    int N;
    cin >> N;
    vector<int> A(N);
    for (int i = 0; i < N; i++) cin >> A[i];
    int l = 0, r = N;
    while (r-l > 1) {
        int c = (l+r)/2;
        map<int, int> mp;
        for (int i = 1; i < N; i++) {
            if (A[i-1] >= A[i]) {
                if (c == 1) {
                    mp[0] = 1;
                    break;
                }
                int t = A[i];
                mp[t]++;
                auto it = mp.upper_bound(t);
                mp.erase(it, mp.end());
                while (t > 0 && mp[t] == c) {
                    mp[t] = 0;
                    mp[t-1]++;
                    t--;
                }
            }
            if (mp[0] > 0) break;
        }
        if (mp[0] == 0) r = c;
        else l = c;
    }
    cout << r << endl;
    return 0;
}
