Problem: You are given a positive (greater than zero) integer n.

You have to represent n as the sum of integers (possibly negative) consisting only of ones (digits '1'). For example, 24 = 11 + 11 + 1 + 1 and 102 = 111 - 11 + 1 + 1. 

Among all possible representations, you have to find the one that uses the minimum number of ones in total.

Input

The single line contains one integer n (1 ≤ n < 10^{50}).

Output

Print one integer x — the minimum number of ones, such that there exist a representation of n as the sum of integers (possibly negative) that uses x ones in total.

Examples

Input


24


Output


6


Input


102


Output


7

Solution (in PYTHON):

Solution:
d={input():0}
for i in range(100,0,-1):
 d,e={},d
 u=10**i/9
 for v,c in e.items():
  for x in range(-6,7):
	t=x*u+v
	if abs(t)<u:d[t]=min(c+i*abs(x),d.get(t,99999))
print d[0]