You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.

Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$

The Fibonacci sequence is a recursive series of integers calculated by

$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$

Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?

Examples

\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match

\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches

Input

1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$

\$ n >= 5\$

Output

1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$

It is acceptable that the program only works accurately until the float precision limit of the language.

Test Cases

Input -> Output
5 -> 1
10 -> 2
12 -> 2
15 -> 5
20 -> 7
23 -> 7
25 -> 9
50 -> 18
100 -> 39

Tips

Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$

Rounding will give you errors.

Let's look at \$n = 5\$ again.

\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.

Useful information and math.

The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.

\$\frac 1 φ = φ -1 \$

\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$

Winning criterion

Code Golf.