func root(a float64, n int) float64 {
    n1 := n - 1
    n1f, rn := float64(n1), 1/float64(n)
    x, x0 := 1., 0.
    for {
        potx, t2 := 1/x, a
        for b := n1; b > 0; b >>= 1 {
            if b&1 == 1 {
                t2 *= potx
            }
            potx *= potx
        }
        x0, x = x, rn*(n1f*x+t2)
        if math.Abs(x-x0)*1e15 < x {
            break
        }
    }
    return x
}