Mr. Yokohama is estimating the delivery fare for a number of luggage pieces. The fare for a piece is determined by its width w, depth d and height h, each rounded up to an integer. The fare is proportional to the sum of them.</p>

The list of the luggage pieces is at hand, but the list has the product w×d×h for each piece, instead of the sum w+d+h by mistake. This information is not enough to calculate the exact delivery fare.

Mr. Yokohama therefore decided to estimate the minimum possible delivery fare. To this end, given the listed product p for each of the luggage pieces, the minimum possible sum s=w+d+h satisfying p=w×d×h should be found.

You are requested to help Mr. Yokohama by writing a program that, when given the product p, computes the minimum sum s.

입력 형식

The input consists of multiple datasets. Each of the datasets has one line containing an integer p (0 < p < 10¹⁵).</p>

The end of the input is indicated by a line containing a zero.

The number of datasets does not exceed 300.

출력 형식

For each dataset, output a single line containing an integer s. s should be the minimum possible sum w+d+h of three positive integers, w, d, and h, satisfying p=w×d×h.

예제 입력

1
2
6
8
729
47045881
12137858827249
562949953421312
986387345919360
999730024299271
999998765536093
0

예제 출력

3
4
6
6
27
1083
6967887
262144
298633
299973
999998765536095