Let's call an array of non-negative integers a_1, a_2, …, a_n a k-extension for some non-negative integer k if for all possible pairs of indices 1 ≤ i, j ≤ n the inequality k ⋅ |i - j| ≤ min(a_i, a_j) is satisfied. The expansion coefficient of the array a is the maximal integer k such that the array a is a k-extension. Any array is a 0-expansion, so the expansion coefficient always exists.

You are given an array of non-negative integers a_1, a_2, …, a_n. Find its expansion coefficient.

Input

The first line contains one positive integer n — the number of elements in the array a (2 ≤ n ≤ 300 000). The next line contains n non-negative integers a_1, a_2, …, a_n, separated by spaces (0 ≤ a_i ≤ 10^9).

Output

Print one non-negative integer — expansion coefficient of the array a_1, a_2, …, a_n.

Examples

Input


4
6 4 5 5


Output


1

Input


3
0 1 2


Output


0

Input


4
821 500 479 717


Output


239

Note

In the first test, the expansion coefficient of the array [6, 4, 5, 5] is equal to 1 because |i-j| ≤ min(a_i, a_j), because all elements of the array satisfy a_i ≥ 3. On the other hand, this array isn't a 2-extension, because 6 = 2 ⋅ |1 - 4| ≤ min(a_1, a_4) = 5 is false.

In the second test, the expansion coefficient of the array [0, 1, 2] is equal to 0 because this array is not a 1-extension, but it is 0-extension.

n = int(input())

l = list(map(int,input().split()))
min_array = []
min_array2 = []
for i in range(int(n/2)):
	if len(min_array) == 0 or min_array[-1] > l[i]:
		min_array.append(l[i])
	else:
		min_array.append(min_array[-1])
for i in range(1,int(n/2)+1):
	if len(min_array2) == 0 or min_array2[-1] > l[-i]:
		min_array2.append(l[-i])
	else:
		min_array2.append(min_array2[-1])
# min_array2 = min_array2[::-1]
r = []
for i in range(len(min_array2)):
	s = (min_array2[i],min_array[i])
	r.append(s)
z = float("inf")
k = float("inf")
# print(min_array,min_array2)
# print(r)
for i in range(len(r)):

	z = min(z,r[i][0],r[i][1])
	k = min(k,int(z/(n-1-i)))

k1 = min(l)/(int(n/2))
print(min(k,k1))
