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 Int = long long;
bool test(const vector<int>& A, int k)
{
    int last = 0;
    if (k == 1) {
        for (int a : A) {
            if (a <= last) return false;
            last = a;
        }
        return true;
    }
    map<int, int> m;
    for (int a : A) {
        if (a <= last) {
            m[a] += 1;
            m.erase(++m.find(a), m.end());
            int b = a;
            while (b > 0 && m[b] >= k) {
                m[b] = 0;
                m[b-1]++;
                b--;
            }
            if (b == 0) return false;
        }
        last = a;
    }
    return true;
}
int main()
{
    int N; cin >> N;
    vector<int> A(N); for (auto& a : A) cin >> a;
    int lo = 0, hi = N;
    while (hi - lo > 1) {
        int mid = (lo + hi) / 2;
        (test(A, mid) ? hi : lo) = mid;
    }
    cout << hi << endl;
    return 0;
}
