from collections import deque


def fib_frog(a: list[int]) -> int:
    size = len(a)

    fib = [0, 1]
    i = 1
    while fib[i] <= size:
        i += 1
        fib.append(fib[i - 1] + fib[i - 2])

    queue = deque([(-1, 0)])
    visited = [False] * size

    while queue:
        idx, jumps = queue.popleft()
        for f in range(len(fib) - 1, 1, -1):
            new_idx = idx + fib[f]
            if new_idx == size:
                return jumps + 1
            if new_idx > size or visited[new_idx] or a[new_idx] == 0:
                continue
            if a[new_idx] == 1:
                visited[new_idx] = True
                queue.append((new_idx, jumps + 1))

    return -1