Problem:
Score : 200 points

Problem Statement

Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.

The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)

Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?

Constraints

101 \le X \le 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.

Sample Input 1

103

Sample Output 1

3

The balance after one year is 101 yen.

The balance after two years is 102 yen.

The balance after three years is 103 yen.

Thus, it takes three years for the balance to reach 103 yen or above.

Sample Input 2

1000000000000000000

Sample Output 2

3760

Sample Input 3

1333333333

Sample Output 3

1706

Solution in Go (1.14.1) (judge verdict: Wrong Answer)

//go:generate echo "https://atcoder.jp/contests/abc165/tasks/abc165_b"
package main

import (
	"bufio"
	"fmt"
	"io"
	"math"
	"math/big"
	"os"
	"strconv"
)

var scan = newScanner(os.Stdin)

func Solve(X float64) int {
	deposit := 100.0
	y := 0
	for deposit < X {
		deposit = math.Trunc(deposit * 1.01)
		y++
	}
	return y
}

func main() {
	X := scan.Float64()
	fmt.Println(Solve(X))
}

type scanner struct {
	*bufio.Scanner
}

func newScanner(r io.Reader) *scanner {
	s := bufio.NewScanner(r)
	s.Split(bufio.ScanWords)
	s.Buffer(nil, 100000000)
	return &scanner{s}
}

func (s *scanner) String() string {
	s.Scan()
	return s.Text()
}

func (s *scanner) Strings(l int) []string {
	if l == 0 {
		return []string{}
	}
	sl := make([]string, l, l)
	for i := range sl {
		sl[i] = s.String()
	}
	return sl
}

func (s *scanner) Int() int {
	n, _ := strconv.Atoi(s.String())
	return n
}

func (s *scanner) Ints(l int) []int {
	if l == 0 {
		return []int{}
	}
	sl := make([]int, l, l)
	for i := range sl {
		sl[i] = s.Int()
	}
	return sl
}

func (s *scanner) Float64() float64 {
	f, _ := strconv.ParseFloat(s.String(), 64)
	return f
}

func (s *scanner) Floats64(l int) []float64 {
	if l == 0 {
		return []float64{}
	}
	sl := make([]float64, l, l)
	for i := range sl {
		sl[i] = s.Float64()
	}
	return sl
}

func (s *scanner) BigInt() *big.Int {
	n, _ := strconv.ParseInt(s.String(), 10, 64)
	return big.NewInt(n)
}

func (s *scanner) BigInts(l int) []*big.Int {
	if l == 0 {
		return []*big.Int{}
	}
	sl := make([]*big.Int, l, l)
	for i := range sl {
		sl[i] = s.BigInt()
	}
	return sl
}

func iabs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func imax(x, y int) int {
	if x > y {
		return x
	}
	return y
}

func imin(x, y int) int {
	if x < y {
		return x
	}
	return y
}

func ipow(x, n int) int {
	if n == 0 {
		return 1
	}
	a := ipow(x, n>>1)
	a *= a
	if n&1 != 0 {
		a *= x
	}
	return a
}

func chmax(x *int, v int) {
	if *x < v {
		*x = v
	}
}

func chmin(x *int, v int) {
	if *x > v {
		*x = v
	}
}

func factor(n int) map[int]int {
	m := map[int]int{}
	for i := 2; i*i <= n; i++ {
		for n%i == 0 {
			n /= i
			m[i]++
		}
	}
	if n != 1 {
		m[n]++
	}
	return m
}

var mod = 1000000007

func setMintMod(x int) {
	mod = x
}

type mint int

func newMint(v int) mint {
	return mint((v%mod + mod) % mod)
}

func (x mint) Add(y mint) mint {
	v := x + y
	if v >= mint(mod) {
		return v - mint(mod)
	}
	return v
}

func (x mint) Sub(y mint) mint {
	v := x + mint(mod) - y
	if v >= mint(mod) {
		return v - mint(mod)
	}
	return v
}

func (x mint) Mul(y mint) mint {
	return (x * y) % mint(mod)
}

func (x mint) pow(n int) mint {
	if n == 0 {
		return mint(1)
	}
	a := x.pow(n >> 1)
	a = a.Mul(a)
	if n&1 != 0 {
		a = a.Mul(x)
	}
	return a
}

func (x mint) Inverse() mint {
	return x.pow(mod - 2)
}

func (x mint) Div(y mint) mint {
	return x * y.Inverse()
}

func (x mint) Neg() mint {
	return newMint(int(-x))
}

type factorial struct {
	fact        []mint
	factInverse []mint
}

func newFactorial(n int) *factorial {
	f := new(factorial)
	f.init(n)
	return f
}

func (f *factorial) init(n int) {
	fact := make([]mint, n+1, n+1)
	fact[0] = newMint(1)
	for i := 1; i <= n; i++ {
		fact[i] = fact[i-1].Mul(newMint(i))
	}

	inv := make([]mint, n+1, n+1)
	inv[n] = fact[n].Inverse()
	for i := n; i >= 1; i-- {
		inv[i-1] = inv[i].Mul(newMint(i))
	}

	f.fact = fact
	f.factInverse = inv
}

func (f *factorial) Get(n int) mint {
	return f.fact[n]
}

func (f *factorial) GetInverse(n int) mint {
	return f.factInverse[n]
}

func (f *factorial) Permutation(n, k int) mint {
	if k < 0 || n < k {
		return 0
	}
	return f.fact[n].Mul(f.factInverse[n-k])
}

func (f *factorial) Combination(n, k int) mint {
	if k < 0 || n < k {
		return 0
	}
	return f.fact[n].Mul(f.factInverse[k]).Mul(f.factInverse[n-k])
}

type sieve struct {
	n          int
	primes     []int
	maxFactors []int
}

func newSieve(n int) *sieve {
	s := &sieve{
		n:          n,
		primes:     []int{},
		maxFactors: make([]int, n+1, n+1),
	}
	s.init()
	return s
}

func (s *sieve) init() {
	s.maxFactors[0] = -1
	s.maxFactors[1] = -1
	for i := 2; i <= s.n; i++ {
		if s.maxFactors[i] != 0 {
			continue
		}
		s.primes = append(s.primes, i)
		s.maxFactors[i] = i
		for j := i * i; j <= s.n; j += i {
			if s.maxFactors[j] == 0 {
				s.maxFactors[j] = i
			}
		}
	}
}

func (s *sieve) IsPrime(x int) bool {
	return s.maxFactors[x] == x
}

func (s *sieve) Factor(x int) map[int]int {
	m := map[int]int{}
	for x != 1 {
		m[s.maxFactors[x]]++
		x /= s.maxFactors[x]
	}
	return m
}