sol1.py

"""
The Fibonacci sequence is defined by the recurrence relation:

 Fn = Fn-1 + Fn-2, where F1 = 1 and F2 = 1.

Hence the first 12 terms will be:

 F1 = 1
 F2 = 1
 F3 = 2
 F4 = 3
 F5 = 5
 F6 = 8
 F7 = 13
 F8 = 21
 F9 = 34
 F10 = 55
 F11 = 89
 F12 = 144

The 12th term, F12, is the first term to contain three digits.

What is the index of the first term in the Fibonacci sequence to contain 1000
digits?
"""


deffibonacci(n: int) ->int:
"""
 Computes the Fibonacci number for input n by iterating through n numbers
 and creating an array of ints using the Fibonacci formula.
 Returns the nth element of the array.

 >>> fibonacci(2)
 1
 >>> fibonacci(3)
 2
 >>> fibonacci(5)
 5
 >>> fibonacci(10)
 55
 >>> fibonacci(12)
 144

 """
ifn==1ornotisinstance(n, int):
return0
elifn==2:
return1
else:
sequence= [0, 1]
foriinrange(2, n+1):
sequence.append(sequence[i-1] +sequence[i-2])

returnsequence[n]


deffibonacci_digits_index(n: int) ->int:
"""
 Computes incrementing Fibonacci numbers starting from 3 until the length
 of the resulting Fibonacci result is the input value n. Returns the term
 of the Fibonacci sequence where this occurs.

 >>> fibonacci_digits_index(1000)
 4782
 >>> fibonacci_digits_index(100)
 476
 >>> fibonacci_digits_index(50)
 237
 >>> fibonacci_digits_index(3)
 12
 """
digits=0
index=2

whiledigits<n:
index+=1
digits=len(str(fibonacci(index)))

returnindex


defsolution(n: int=1000) ->int:
"""
 Returns the index of the first term in the Fibonacci sequence to contain
 n digits.

 >>> solution(1000)
 4782
 >>> solution(100)
 476
 >>> solution(50)
 237
 >>> solution(3)
 12
 """
returnfibonacci_digits_index(n)


if__name__=="__main__":
print(solution(int(str(input()).strip())))