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 main():
    n = int(input())
    a = list(map(int, input().split()))
    for i in range(n-1):
        if a[i] >= a[i+1]:
            break
    else:
        print(1)
        return

    def value(kind):
        length = 0
        d = dict()
        for i in a:
            if length >= i:
                del_list = []
                for j in d:
                    if j > i:
                        del_list.append(j)
                for j in del_list:
                    d.pop(j)
                for j in range(i, 0, -1):
                    if j not in d:
                        d[j] = 2
                        break
                    else:
                        if d[j] < kind:
                            d[j] += 1
                            break
                        else:
                            d.pop(j)
                else:
                    return False
            length = i
        return True

    ok, ng = n, 1
    while abs(ok-ng) > 1:
        mid = (ok+ng)//2
        if value(mid):
            ok = mid
        else:
            ng = mid
    print(ok)


main()
