def rotate(x, n, d):
    if x - d < 1:
        return x - d + n
    elif x + d > n:
        return x + d - n
    else:
        return x - d

def palindrome_ops(w, n, d):
    # generate all palindromes
    mid = (w + 1) // 2
    if w % 2 == 0:
        palindromes = [(i,) * mid for i in range(1, n+1)]
    else:
        palindromes = [(i,) * (mid - 1) + (j,) + (i,) * (mid - 1)
                       for i in range(1, n+1) for j in range(1, n+1)]
    # calculate minimum operations for each palindrome
    min_ops = float('inf')
    for p in palindromes:
        ops = 0
        for i in range(mid):
            if p[i] != p[w-i-1]:
                diff = abs(p[i] - p[w-i-1])
                ops += min(diff, n-diff) // d
        min_ops = min(min_ops, ops)
    return min_ops if min_ops != float('inf') else -1