Consider the natural numbers from 1 to N. By associating to each number a sign (+ or -) and calculating the value of this expression we obtain a sum S. The problem is to determine for a given sum S the minimum number N for which we can obtain S by associating signs for all numbers between 1 to N.
For a given S, find out the minimum value N in order to obtain S according to the conditions of the problem.
The only line contains in the first line a positive integer S (0< S <= 100000) which represents the sum to be obtained.
The output will contain the minimum number N for which the sum S can be obtained.
The sum 12 can be obtained from at least 7 terms in the following way: 12 = -1+2+3+4+5+6-7.