package main


import (
	"fmt"
	"math"
	"math/bits"
	"strconv"
)

func smallestGoodBase(n string) string {
	nVal, _ := strconv.Atoi(n)
	mMax := bits.Len(uint(nVal)) - 1
	// k < n^(-s) < k + 1
	for m := mMax ; m > 1 ; m -- {
		k := int( math.Pow(float64(nVal), 1/float64(m)))
		sum := 1
		for i := 0 ; i < m ; i ++ {
			sum = sum * k + 1
		}
		if sum == nVal {
			return strconv.Itoa(k)
		}
	}
	return strconv.Itoa(nVal - 1)
}

func main() {
	fmt.Println(smallestGoodBase("13"))
}