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
import random
input()
A = [int(_) for _ in input().split()]
A = [A[0]] + [j for i, j in zip(A, A[1:]) if i >= j]
N = len(A)


def cut(array, index):
    if index < 1:
        return []
    if index <= array[0][0]:
        return [(index, array[0][1])]
    for _ in range(len(array)-1, 0, -1):
        if array[_ - 1][0] < index:
            return array[:_] + [(index, array[_][1])]


def is_possible(K):
    dp = [(A[0], 0)]
    for a in A[1:]:
        if a <= dp[-1][0]:
            dp = cut(dp, a)
        else:
            dp += [(a, 0)]
        is_added = False
        for j in range(len(dp) - 1, -1, -1):
            if dp[j][1] < K - 1:
                dp = cut(dp, dp[j][0] - 1) + [(dp[j][0], dp[j][1] + 1)]
                if dp[-1][0] < a:
                    dp += [(a, 0)]
                is_added = True
                break
        if not is_added:
            return False
    return True


def bis(x, y):
    if y == x + 1:
        return y
    elif is_possible((x + y) // 2):
        return bis(x, (x + y) // 2)
    else:
        return bis((x + y) // 2, y)


print(bis(0, N))
