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 (Python):

import re
import math
from collections import defaultdict
import itertools
from copy import deepcopy
import random
from heapq import heappop,heappush
import time
import os
import queue
import sys
import datetime
from functools import lru_cache

readline=sys.stdin.readline
sys.setrecursionlimit(2000)

alphabet="abcdefghijklmnopqrstuvwxyz"
mod=int(10**9+7)
inf=int(10**20)
def yn(b):
    if b:
        print("yes")
    else:
        print("no")
def Yn(b):
    if b:
        print("Yes")
    else:
        print("No")
def YN(b):
    if b:
        print("YES")
    else:
        print("NO")
class union_find():
    def __init__(self,n):
        self.n=n
        self.P=[a for a in range(N)]
        self.rank=[0]*n
 
    def find(self,x):
        if(x!=self.P[x]):self.P[x]=self.find(self.P[x])
        return self.P[x]
 
    def same(self,x,y):
        return self.find(x)==self.find(y)
 
    def link(self,x,y):
        if self.rank[x]<self.rank[y]:
            self.P[x]=y
        elif self.rank[y]<self.rank[x]:
            self.P[y]=x
        else:
            self.P[x]=y
            self.rank[y]+=1
 
    def unite(self,x,y):
        self.link(self.find(x),self.find(y))
 
    def size(self):
        S=set()
        for a in range(self.n):
            S.add(self.find(a))
        return len(S)
def is_power(a,b):
    now=b
    while now<a:
        now*=b
    if now==a:return True
    else:return False
def bin_(num,size):
    A=[0]*size
    for a in range(size):
        if (num>>(size-a-1))&1==1:
            A[a]=1
        else:
            A[a]=0
    return A
def get_facs(n,mod_=0):
    A=[1]*(n+1)
    for a in range(2,len(A)):
        A[a]=A[a-1]*a
        if(mod>0):A[a]%=mod_
    return A
def comb(n,r,mod,fac):
    if(n-r<0):return 0
    return (fac[n]*pow(fac[n-r],mod-2,mod)*pow(fac[r],mod-2,mod))%mod
def next_comb(num,size):
    x=num&(-num)
    y=num+x
    z=num&(~y)
    z//=x
    z=z>>1
    num=(y|z)
    if(num>=(1<<size)):return False
    else:
        return num
def get_primes(n,type="int"):
    A=[True]*(n+1)
    A[0]=False
    A[1]=False
    for a in range(2,n+1):
        if A[a]:
            for b in range(a*2,n+1,a):
                A[b]=False
    if(type=="bool"):return A
    B=[]
    for a in range(n+1):
        if(A[a]):B.append(a)
    return B
def is_prime(num):
    if(num<=2):return False
    i=2
    while i*i<=num:
       if(num%i==0):return False
       i+=1
    return True
def ifelse(a,b,c):
    if a:return b
    else:return  c
def join(A,c=" "):
    n=len(A)
    A=list(map(str,A))
    s=""
    for a in range(n):
        s+=A[a]
        if(a<n-1):s+=c
    return s
def factorize(n,type_="dict"):
    b = 2
    list_ = []
    while b * b <= n:
        while n % b == 0:
            n //= b
            list_.append(b)
        b+=1
    if n > 1:list_.append(n)
    if type_=="dict":
        dic={}
        for a in list_:
            if a in dic:
                dic[a]+=1
            else:
                dic[a]=1
        return dic
    elif type_=="list":
        return list_
    else:
        return None
def floor_(n,x=1):
    return x*(n//x)
def ceil_(n,x=1):
    return x*((n+x-1)//x)
def hani(x,min_,max_):
    ret=x
    if x<min_:ret=min_
    if x>max_:ret=max_
    return ret
def seifu(x):
    return x//abs(x)

def main():
    x=int(input())
    now=100
    ans=0
    while now<x:
        now*=1.01
        now//=1
        ans+=1
    print(ans)

main()

Solution (Python):
X = int(input())
p = 100
i = 0

while(True):
    i += 1
    p = int(p*(1.01))
    if X <= p:
        print(i)
        break

Solution (Python):
if __name__ == '__main__':
	X = int(input())
	y = 0
	m = 100
	while m < X:
		m = m + (m//100)
		y += 1
	print(y)

Solution (Python):
x = int(input())
a = 100
count = 0
while a < x:
    a = int(a*1.01)
    count += 1
    
print(count)

Solution (Python):
n = int(input())
x = 100
ret = 0
while x < n:
    x = int(x*1.01)
    ret+=1
print(ret)

Solution (Python):
X = int(input())
money = 100
count = 0
while True:
    money += int(money * 0.01)
    count += 1
    if money >= X:
        break

print(count)

Solution (Python):
x = int(input())
n = 100
y = 0
while n < x:
    n += n//100
    y += 1
print(y)

Solution (Python):
x = int(input())
a = 100
c = 0

while x > a:
    a = int(a*1.01)
    c += 1
print(c)

Solution (Python):
x = int(input())
p = 100
count = 0
while p < x:
    p = p + (p // 100)
    count -= -1
print(count)

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz')
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    
    
    X = r_int()
    i = 100
    cnt = 0
    while True:
        cnt += 1
        i = floor(i * 1.01)
        if i >= X:
            print(cnt)
            return
    
    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
X=int(input())
a=100
for i in range(4000):
  a*=1.01
  a//=1
  if a>=X:
    print(i+1)
    exit()

Solution (Python):
X = int(input())

m = 100
ans = 0

while(m < X):
    m *= 1.01
    ans += 1
    m = int(m)

print(ans)

Solution (Python):
import sys
def main():
    x = int(input())
    c = 0
    m = 100
    while True:
        m = (m * 1.01)//1
        c += 1
        if m >= x:
            print(c)
            sys.exit()
if __name__ == '__main__':
    main()

Solution (Python):
x = int(input())

ret = 0
now = 100

while True:
    now = now + (now // 100)
    ret += 1
    if now >= x:
        print(ret)
        break

Solution (Python):
x = int(input())
value = 100
count = 0

while value < x:
    value *= 1.01
    value = int(value)
    count += 1

print(count)

Solution (Python):

import os
import sys
from io import BytesIO, IOBase


def main():
    m=int(input())
    cnt=0
    n=100
    while n<m:
        cnt+=1
        n=n+n//100
    print(cnt)




BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")


if __name__ == "__main__":
    main()

Solution (Python):
def input_int():
    return map(int, input().split())

def one_int():
    return int(input())

def one_str():
    return input()

def many_int():
    return list(map(int, input().split()))

X=one_int()

count = 0
money =100
hukuri = 0.01
while True:
    count+=1
    money = int(money + money*hukuri)
    if int(money)>=X:
        break
print(count)

Solution (Python):
X = int(input())
XX = 100
Y = 0
while X > XX:
    XX = int(XX * 1.01)
    Y += 1

print(Y)

Solution (Python):
x=int(input())
num=100
ans=0
while num<x:
    num*=(1.01)
    num=int(num)
    ans+=1
print(ans)

Solution (Python):
x=int(input())
s=100
i=0
while s<x:
  s+=s//100
  i+=1
print(i)

Solution (Python):
X=int(input())
m = 100
count =1
while True:
    m = int(m*1.01)
    if m >= X:
        print(count)
        break
    count += 1

Solution (Python):
X=int(input())
bank = 100
count=0
while X>bank:
    bank=int(1.01*bank)
    count+=1
print(count)

Solution (Python):
n=int(input())
x=100
ans=0
while x<n:
  x*=1.01
  x//=1
  ans+=1
print(ans)

Solution (Python):

X = int(input())

base = 1.01
cur = 100
for i in range(1, 100000000000000):
    cur *= base
    cur = int(cur)
    if cur >= X:
        print(i)
        break

Solution (Python):
n = int(input())
ans=100
c=0
while(ans<n):
    ans+=int(ans/100)
    c+=1
print(c)

Solution (Python):
x = int(input())
res = 100
t = 0
while res < x:
    res *= 1.01
    res = int(res)
    t += 1
print(t)

Solution (Python):
import sys
readline = sys.stdin.readline

X = int(readline())

i = 0
a = 100
while True:
    i += 1
    a = int(a * 1.01)
    if a >= X:
        print(i)
        exit(0)

Solution (Python):
x = int(input())




money = 100
year = 0
while money < x:
    money *= 1.01
    money = money//1
    year += 1

print(year)

Solution (Python):
X = int(input())

n = 100
cnt = 0
while n < X:
    n = int(n * 1.01)
    cnt += 1
print(cnt)

Solution (Python):
(X, ) = [int(n) for n in input().split()]

N = 100
ans = 0
while N < X:
    N = (N * 101) // 100
    ans += 1

print(ans)

Solution (Python):
def main():
    X = int(input())
    s = 100
    cnt = 0
    while s < X:
        s = int(s * 1.01)
        cnt += 1
    print(cnt)

if __name__ == '__main__':
    main()

Solution (Python):
import sys
input = sys.stdin.readline
X = int(input())
t = 100
for i in range(1, 10000):
  t = int(t * 1.01)
  if t >= X:
    print(i)
    break

Solution (Python):

import numpy as np
from collections import deque
x = int(input())
money = 100
year = 0
while x > money:
    money = int(money*1.01)
    year += 1
print(year)

Solution (Python):
X=int(input())

M=100
for i in range(1,10**7):
    M=int(M*1.01)
    if M>=X:
        print(i)
        exit()

Solution (Python):
import math


X = int(input())
money = 100
result = 0
while money < X:
    result += 1
    money += math.floor(money*0.01)

print(result)

Solution (Python):
X = int(input())

ans = 100
i = 1
while True:
    ans = int(ans*1.01)
    if ans >= X:
        print(i)
        exit()
    else:
        i += 1

Solution (Python):
def main():
    x = int(input())
    m = 100
    y = 0
    while m<x:
        y += 1
        m = int(m*1.01)
    print(y)


if __name__ == "__main__":
    main()

Solution (Python):
def resolve():
    x = int(input())
    a = 100
    for i in range(1, 3761):
        a = int(a * 1.01)
        if a >= x:
            print(i)
            break

if __name__ == '__main__':
    resolve()

Solution (Python):
x = int(input())

mon = 100
year = 0
while mon < x:
    profit = int(mon * 0.01)
    mon += profit
    year += 1

print(year)

Solution (Python):
X = int(input())
x = 100
for i in range(1000000):
    x = int(x * 1.01)
    if x >= X:
        print(i+1)
        break

Solution (Python):
X = int(input())
num = 100
count = 0
while True:
    count += 1

    num = num + int(num * 0.01)

    if num >= X:
        break

print(count)

Solution (Python):
import sys
X=int(input())

ans = 0
nedan = 100

while True:
    ans += 1

    nedan = nedan + (nedan // 100)

    if X <= nedan:
        break

print(ans)

Solution (Python):
from sys import stdin
X = int(stdin.readline().rstrip())
tmp = 100
for i in range(1,5000):
    tmp += int(tmp*0.01)
    if tmp >= X:
        print(i)
        break

Solution (Python):
input = raw_input

x = int(input())

cur = 100
out = 0

while cur < x:
    cur = int(cur * 1.01)
    out += 1

print(out)

Solution (Python):
import math
x = int(input())
n = 100
i = 0
while n < x:
  i += 1
  n = math.floor(n*1.01)
print(i)

Solution (Python):
X = int(input())
x = 100
count = 0
for i in range(10**18):
    x = int(x*1.01)
    count += 1
    if x>=X:
        print(count)
        break

Solution (Python):
x=100
d=int(input())
ans=0

while 1:
  if x>=d:
    print(ans);exit()
  ans+=1
  x+=x//100

Solution (Python):
X = int(input())
M = 100
y = 0
while M < X:
    M += int(M * 0.01)
    y += 1
print(y)

Solution (Python):
x = int(input())
a = 100
count = 0
while a < x:
    count+=1
    a += (a//100)
print(count)

Solution (Python):
X=int(input())
n=100
i=0
while n<X:
  n=int(n*1.01)
  i+=1
print(i)

Solution (Python):
X = int(input())
p = 100
c = 0
while p < X:
    c += 1
    p = int(p*1.01)
print(c)

Solution (Python):
import math
x = int(input())
cnt = 0
money = 100
while money<x:
  money = math.floor(money*1.01)
  cnt += 1
print(cnt)

Solution (Python):
X = int(input())
tmp = 100
count = 0
while tmp < X:
    tmp += int(tmp * 0.01)
    count +=1
print(count)

Solution (Python):
x = int(input())

m = 100

y = 0
while True:
	if m >= x:
		print(y)
		exit()
	m = int(m * 1.01)
	y += 1

Solution (Python):
import math
X = int(input())
c = 100
cnt = 0

while True:
    cnt += 1
    c = math.floor(c*1.01)
    if X <= c:
        print(cnt)
        break

Solution (Python):
x = int(input())

a = 100
ans = 0
while a < x:
    a = int(a * 1.01)
    ans += 1

print(ans)

Solution (Python):
X = int(input())
a = 100
ans = 0
while a < X:
	ans += 1
	a = int(a * 1.01)
print(ans)

Solution (Python):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil
from operator import itemgetter
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [[LI()]for i in range(n)]
inf = 10**17
mod = 10**9 + 7


x=I()
pr=100
for i in range(100000):
    pr=int(pr*1.01)
    if pr>=x:
        print(i+1)
        sys.exit()

Solution (Python):


import sys
input= lambda: sys.stdin.readline().rstrip()
def pin(type=int):return map(type,input().split())
def tupin(t=int):return tuple(pin(t))

def resolve():
    N,=pin()
    temp=100
    for i in range(1,1000000):
        temp=(temp*1.01)//1
        
        if temp>=N:
            print(i)
            break

resolve()

Solution (Python):
x = int(input())

year = 0
n = 100

while n < x:
    n = int(n * 1.01)
    year += 1

print(year)

Solution (Python):
import math
x = int(input())
k = 100
y = 1.01
ans = 0
while k < x:
    ans += 1
    k = math.floor(k * 1.01)
print(ans)

Solution (Python):
x = int(input())
cnt = 0
m = 100
while m < x:
  m = int(m * 1.01)
  cnt += 1
print(cnt)

Solution (Python):
x=int(input())

money=100
cnt=0
while(True):
    risi = money // 100
    money+=risi
    cnt+=1
    if money>=x:
        print(cnt)
        exit()

Solution (Python):
X = int(input())
K = 100
for i in range(1, 10000000000):
    K = int(K * 1.01)
    if K >= X:
        print(i)
        exit()

Solution (Python):



def compound_interest(principle, rate, time): 
  
    
    CI = int(principle * (pow((1 + rate / 100), time)))
    return CI
    
x=int(input())
principle=100
res=0
while principle<x:
    principle=compound_interest(principle,1,1)
    res+=1
print(res)

Solution (Python):
x = int(input())

ans = 0
_x = 100
while _x < x:
    _x = _x * 1.01 // 1
    ans += 1

print(ans)

Solution (Python):
x = int(input())
a = 100
cnt = 0
while True:
	a += int(a*0.01)
	cnt += 1
	if a  >= x:
		break
print (cnt)

Solution (Python):
x=int(input())
m=100
t=1.01
ans=0
while x>m:
    ans+=1
    m=int(m*t)
print(ans)

Solution (Python):

"""
Created on Sat May  2 20:55:50 2020

@author: Kanaru Sato
"""

x = int(input())
count = 0
yokin = 100

while yokin < x:
    count += 1
    yokin *= 1.01
    yokin = int(yokin)
    
print(count)

Solution (Python):
X = int(input())

money = 100
count = 0
while True:
    count += 1
    money += int(money*(0.01))
    if money >= X:
        print(count)
        exit()

Solution (Python):
x = int(input())
ans = 0
now = 100
while (now < x):
    ans += 1
    now += int(now*0.01)
print(ans)

Solution (Python):
x = int(input())
year = 0
m = 100

for i in range(100000):
    m = int(m*1.01)
    year += 1
    if m >= x:
        print(year)
        exit()

Solution (Python):
X=int(input())
ans=0
a=100
while a<X:
    a+=a//100
    ans+=1
print(ans)

Solution (Python):
import math
x = int(input())

c = 100
ans = 0
while c < x:
    c = math.floor(c * 1.01)
    ans += 1

print(ans)

Solution (Python):
x = int(input())
import math
a = 100
count = 0
while a < x:
  a = math.floor(a* 1.01)
  count += 1
 
print(count)

Solution (Python):

def main():
    X = int(input())
    N = 100
    ans = 0
    while True:
        N += int(N*0.01)
        ans += 1
        if N >= X:
            break
            
    print(ans)


if __name__ == "__main__":
    main()

Solution (Python):
x = int(input())



y = 100
a = 1
while True:
    y = int(y*1.01)
    if y >= x:
        
        print(a)
        exit()
    a += 1

Solution (Python):
X = int(input())
R = 100
ans = 0
for i in range(1, 5000):
    R *= 1.01
    R = int(R)
    if X <= R:
        ans = i
        break
print(ans)

Solution (Python):
count = 0
x = int(input())
money = 100
while True:
    count += 1
    money = int(money*1.01)
    if money >= x:
        print(count)
        exit()

Solution (Python):
x=int(input())
m=100
for i in range(10**8):
  m*=1.01
  m//=1
  if m>=x:
    print(i+1)
    break

Solution (Python):
from math import floor

def main():
    X=int(input())
    tmp=100
    for year in range(1,4000):
        tmp *= 1.01
        tmp = floor(tmp)
        if tmp >= X:
            print(year)
            exit()

main()

Solution (Python):
X = int(input())
a = 100
cnt = 0
while a<X:
    a = int(a*1.01)
    cnt+=1
print(cnt)

Solution (Python):
x = int(input())
a = 100
num = 0
while (a * 101) // 100 < x:
    a = (a * 101) // 100
    num += 1
print(num + 1)

Solution (Python):
import math
X=int(input())
a=0
o=100
while True:
  o*=1.01
  o=math.floor(o)
  a+=1
  if o>=X:
    print(a)
    break

Solution (Python):
import math
x = int(input())
n = 100
for i in range(1, 3761):
    n = math.floor(n * 1.01)
    if n >= x:
        print(i)
        break

Solution (Python):
n=int(input())
k=100
cnt=0
while k<n:
  cnt+=1
  k=int(k*1.01)
print(cnt)

Solution (Python):
X=int(input())
p=100;ytd=0
while p<X:
  p=int(p*1.01)
  ytd=ytd+1
print(ytd)