F_n is the n-th Fibonacci number defined by the recurrence relation F_n = F_n-1 + F_n-2 with F₁ = F₂ = 1. If n is a perfect square and n > 4, then find the value of the determinant below

| F₁          F₂          ... F_√n  |
| F_√n+1     F_√n+2    ... F_2√n |
|    .           .                .    |
|    .           .                .    |
| F_n-√n+1   F_n-√n+2  ... F_n   |