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 sys
input = sys.stdin.readline

N = int(input())
A = list(map(int, input().split()))
lb, ub = 0, N
while ub - lb > 1:
    m = (lb + ub) // 2
    stack = []
    for a in A:
        if not stack or stack[-1][0] < a:
            stack.append([a, 1])
        elif stack[-1][0] == a:
            stack[-1][1] += 1
        else:
            cur, cnt = stack.pop()
            while stack and stack[-1][0] >= a:
                b, c = stack.pop()
                # cnt = ceil(cnt / m**(cur - b)) + c - 1
                x = 1
                if m > 1:
                    for i in range(cur - b):
                        if x >= cnt:
                            break
                        x *= m
                cnt = (cnt + x - 1) // x + c - 1
                cur = b
            if cur > a:
                # cnt = ceil(cnt / m**(cur - a))
                x = 1
                if m > 1:
                    for i in range(cur - a):
                        if x >= cnt:
                            break
                        x *= m
                cnt = (cnt + x - 1) // x
            stack.append([a, cnt + 1])
    cur, cnt = stack.pop()
    while stack:
        b, c = stack.pop()
        # cnt = ceil(cnt / m**(cur - b)) + c - 1
        x = 1
        if m > 1:
            for i in range(cur - b):
                if x >= cnt:
                    break
                x *= m
        cnt = (cnt + x - 1) // x + c - 1
        cur = b
    # if cnt <= m**cur, ok
    x = 1
    if m > 1:
        for i in range(cur):
            if x >= cnt:
                break
            x *= m
    if cnt <= x:
        ub = m
    else:
        lb = m
print(ub)
