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
from math import log
k=int(input())
step_lst=[]
k_min=k
i=5*int(log(k)/log(10))
if k!=1:
    while i <(2**(k_min)+1):
        count=0
        coord=[1,1]
        for j in bin(i)[2:]:
            count+=1
            v=int(j)
            coord[0]=coord[0]+v*coord[1]
            coord[1]=coord[0]*(1-v)+coord[1]
            if max(coord)>k:
                break
            elif max(coord)==k:
                k_min=count
                k_min=min(k,k_min)
                step_lst.append(count)
        i+=1
    print(min(step_lst))
else:
    print(0)
