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
def is_possible(x, A):
    current = {}
    length = 0
    for a in A:
        if a <= length:
            if x == 1:
                return False
            current = {k: current[k] for k in current if k < a}
            i = a - 1
            if i not in current:
                current[i] = 0
            current[i] += 1
            while i in current and current[i] >= x:
                if i == 0:
                    return False
                if (i-1) not in current:
                    current[i-1] = 0
                current[i-1] += 1
                del current[i]
                i -= 1
        length = a

    return True


def main():
    N = int(input())
    A = list(map(int, input().split()))
    left = 1
    right = N
    while left < right:
        center = (left + right) // 2
        if is_possible(center, A):
            right = center
        else:
            left = center + 1
    print(left)


if __name__ == "__main__":
    main()
