Let's assume that we have a pair of numbers (*a*, *b*). We can get a new pair (*a* + *b*, *b*) or (*a*, *a* + *b*) from the given pair in a single step.

Let the initial pair of numbers be (1,1). Your task is to find number *k*, that is, the least number of steps needed to transform (1,1) into the pair where at least one number equals *n*.
The input contains the only integer *n* (1 ≤ *n* ≤ 10<sup class="upper-index">6</sup>).
5
3
1
0
2
1
3
2
4
3
10
5
1009
15
2009
17
7009
19
9009
20
19009
21
29009
22
12434
21
342342
28
342235
28
362235
28
762235
30
878235
30
978235
30
1000000
30
6
5
10000
20
999999
30
524287
29
777777
30
123756
26
976438
30
434563
28
345634
28
65457
24
123456
26
999997
30
98989
25
8
4
123455
26
990001
30
123141
26
998
16
453422
28
623423
29
89
9
24234
23
999879
30
345612
28
998756
30
999989
30
999998
30
999912
30
100000
25
import math as m

def hcf(a,b):
    while(a!=b):
        if(a>b): a=a-b
        else: b = b-a
    return a
    
n = int(input())
mnm = m.inf
    
for k in range(m.ceil(n/2),n):
    if(hcf(n,k)!=1): continue
    
    p =k
    q = n-k
    count = 2
    while(p!=2):
        diff = p-q
        if(q>diff): 
            p=q
            q=diff
            
        else:
            p=diff
            
        count+=1
        
    if(count<mnm):
        mnm = count
        
print(mnm)
            