#include <stdio.h>
#include <math.h>
#include <cstdlib>
#include <vector>
#include <cmath>
#include <string>
#define base 1000000000
#define base2 ((ull) base * base)
#define KARATSUBA 11111
#define fix(x) {x.resize(x[0]+3); x[x[0]+1]=x[x[0]+2]=0;}
#define ull unsigned long long
using namespace std;
int nrdiv=0;
class BigInt{
public:
vector <unsigned> a;
int semn;
BigInt();
BigInt(long long nr);
BigInt(vector<unsigned> b);
BigInt& operator+=(const BigInt &b);
BigInt& operator+=(long long k);
friend BigInt operator+(const BigInt &x, const BigInt &y);
friend BigInt operator-(const BigInt &x, const BigInt &y);
BigInt& operator*=(int k);
friend BigInt operator*(const BigInt &x, const BigInt &y);
friend BigInt operator/(const BigInt &x, const BigInt &y);
friend BigInt operator%(const BigInt &x, const BigInt &y);
BigInt& operator/=(int k);
int operator%(int k);
friend int operator==(const BigInt &x, const BigInt &y);
friend int operator!=(const BigInt &x, const BigInt &y);
friend int operator<(const BigInt &x, const BigInt &y);
friend int operator<=(const BigInt &x, const BigInt &y);
friend int operator>(const BigInt &x, const BigInt &y);
friend int operator>=(const BigInt &x, const BigInt &y);
void shr(unsigned k);
void shl(unsigned k);
void write(FILE *f) const;
void read(FILE *f);
};
BigInt::BigInt()
{
semn=0;
a.resize(4);
a[0]=1;
}
BigInt::BigInt(long long nr)
{
if (nr<0) semn=-1, nr=-nr; else semn=1;
if (!nr) semn=0;
unsigned long long k=nr;
a.resize(1);
while (k>=base) a.push_back(k%base), k/=base;
a.push_back(k);
a[0]=a.size()-1;
fix(a);
}
BigInt::BigInt(vector <unsigned> b)
{
*this=0;
b.push_back(0);
int nr=b.size()*32-1;
while (nr%29) nr--;
while (nr){
*this*=(1<<29);
//mai baga ceva aici :)
nr-=29;
}
}
void BigInt::shr(unsigned k)
{
if (k>a[0]) k=a[0];
unsigned i;
for (i=1; i<=a[0]-k; i++)
a[i]=a[i+k];
a[0]-=k;
if (!a[0]) a[0]=1, a[1]=1;
fix(a);
}
void BigInt::shl(unsigned k)
{
unsigned i;
a[0]+=k;
a.resize(a[0]+2);
for (i=a[0]; i>k; i--)
a[i]=a[i-k];
memset(&a[1], 0, 4*k);
}
BigInt& BigInt::operator+=(const BigInt &b)
{
if (this == &b){ //in cazul ca in care fac a+=a;
unsigned i, n=a[0]+1;
for (i=1; i<n; i++)
a[i]+=a[i];
for (i=1; i<n; i++)
if (a[i]>=base) a[i]-=base, a[i+1]++;
if (a[n]) a[0]++;
return *this;
}
unsigned i, n=b.a[0]+1;
for (i=1; i<n; ++i)
if (a[i]+b.a[i]>=base) a[i]+=(b.a[i]-base), a[i+1]++; else a[i]+=b.a[i];
if (a[n]) n++;
if (n-1>a[0]) a[0]=n-1;
fix(a);
return *this;
}
BigInt operator+(const BigInt &x, const BigInt &y)
{
if (x.semn==0) return y;
if (y.semn==0) return x;
BigInt rez;
const unsigned *a, *b, *c;
if (x.semn==y.semn){
rez.semn=x.semn;
if (x.a[0]>y.a[0]) a=&x.a[0], b=&y.a[0]; else a=&y.a[0], b=&x.a[0];
unsigned n=a[0]+1, m=b[0]+1;
rez.a.resize(a[0]+2);
memcpy(&rez.a[0], a, sizeof(unsigned) * (n+1));
for (unsigned i=1; i<m; i++){
rez.a[i]+=b[i];
if (rez.a[i]>=base) rez.a[i]-=base, ++rez.a[i+1];
}
unsigned k=m;
while (rez.a[k]>=base) rez.a[k]-=base, ++k, ++rez.a[k];
if (rez.a[a[0]+1]) rez.a[0]++;
fix(rez.a);
if (rez.a[0]==1 && rez.a[1]==0) rez.semn=0;
return rez;
}
rez.semn=x.semn;
if (x.semn>=0) a=&x.a[0], b=&y.a[0]; else a=&y.a[0], b=&x.a[0];
unsigned i, n, m, ok=1;
if (b[0]>a[0]) ok=0;
if (a[0]==b[0])
for (i=a[0]; i>0; i--){
if (a[i]!=b[i]){
ok=(a[i]>b[i]);
break;
}
}
if (!ok) c=a, a=b, b=c, rez.semn=-x.semn;
m=b[0]+1;
rez.a.resize(a[0]+3);
memcpy(&rez.a[0], a, 4*(a[0]+1));
for (i=1; i<m; i++){
if (rez.a[i]>base) rez.a[i]+=base, --rez.a[i+1];
rez.a[i]-=b[i];
if (rez.a[i]>base) rez.a[i]+=base, --rez.a[i+1];
}
while (rez.a[i]>base) rez.a[i]+=base, ++i, --rez.a[i];
n=rez.a[0];
while (n>1 && rez.a[n]==0) --n;
rez.a[0]=n;
fix(rez.a);
if (rez.a[0]==1 && rez.a[1]==0) rez.semn=0;
return rez;
}
BigInt operator-(const BigInt &x, const BigInt &y)
{
BigInt a=y;
a.semn*=-1;
return x+a;
}
BigInt& BigInt::operator+=(long long nr)
{
fix(a);
if (a.size()<5) a.resize(5);
ull k = nr, poz=1;
while (k>=base){
a[poz]+=k%base;
k/=base;
if (a[poz]>=base) a[poz]-=base, ++a[poz+1];
poz++;
}
a[poz]+=k;
if (a[poz]>=base) a[poz]-=base, ++a[poz+1];
if (a[a[0]+1]) a[0]++;
fix(a);
return *this;
}
BigInt& BigInt::operator*=(int nr)
{
if (nr<0) semn=-semn, nr=-nr;
ull num, k=nr;
unsigned i;
for (i=a[0]; i>0; i--){
num=a[i] * k;
unsigned cat = num/base;
a[i]=num - (ull)cat*base;
a[i+1]+=cat;
if (a[i]>=base) a[i]-=base, a[i+1]++;
}
if (a[a[0]+1]) a[0]++;
while (a[0]>1 && !a[a[0]]) --a[0];
fix(a);
return *this;
}
BigInt operator*(const BigInt &x, const BigInt &y)
{
const unsigned *a, *b;
if (x.a[0]>y.a[0]) a=&x.a[0], b=&y.a[0]; else a=&y.a[0], b=&x.a[0];
unsigned n=a[0]+1, m=b[0]+1, i, j, k;
unsigned limit=75*n/100;
if (m>KARATSUBA && m<limit){
m--; n--;
BigInt rez, A, B;
A.a.resize(m+3);
rez.a.resize(n+m+3);
const BigInt *C;
if (x.a[0]>y.a[0]) C=&y; else C=&x;
A.a[0]=m;
k=1;
while (k<=n){
if (k+m-1>n){
A.a[0]=n-k+1; fix(A.a);
}
memcpy(&A.a[1], a+k, 4*A.a[0]);
B=A*(*C);
for (i=1; i<=B.a[0]; i++){
rez.a[i+k-1]+=B.a[i];
if (rez.a[i+k-1]>=base) rez.a[i+k-1]-=base, ++rez.a[i+k];
}
k+=m;
}
n+=m;
while (n>1 && !rez.a[n]) --n;
rez.a[0]=n;
rez.semn=x.semn*y.semn;
fix(rez.a);
return rez;
}
if (n>KARATSUBA && m>=limit){ //Karatsuba
BigInt x1, x2, y1, y2, A, B, C;
unsigned p=(n+m)/4;
x2.a.resize(p+4);
x2.a[0]=p;
memcpy(&x2.a[1], a+1, 4*p);
x1.a.resize(n-p+4);
x1.a[0]=n-p-1;
memcpy(&x1.a[1], a+p+1, 4*(n-p-1));
y2.a.resize(p+4);
y2.a[0]=p;
memcpy(&y2.a[1], b+1, 4*p);
y1.a.resize(m-p+4);
y1.a[0]=m-p-1;
memcpy(&y1.a[1], b+p+1, 4*(m-p-1));
A=x1*y1;
B=x2*y2;
C=(x1+x2)*(y1+y2)-A-B;
A.shl(2*p);
memcpy(&A.a[1], &B.a[1], sizeof(unsigned)*2*p);
C.shl(p);
A+=C;
A.semn=x.semn*y.semn;
fix(A.a);
return A;
}
vector <ull> sol(n+m+1);
sol[0]=n+m-3;
for (i=1; i<m; i++)
for (j=1, k=i; j<n; ){
#define W sol[k] += (ull) b[i] * a[j++]; if (sol[k]>=base2) sol[k]-=base2, ++sol[k+2]; k++;
W W W
}
BigInt rez;
rez.a.resize(sol[0]+3);
for (i=0; i<n+m; i++)
if (sol[i]>=base2) sol[i]-=base2, ++sol[i+2];
for (i=0; i<n+m; i++){
unsigned cat=sol[i]/base;
sol[i+1]+=cat;
rez.a[i]=sol[i]-cat*(ull)base;
}
if (rez.a[rez.a[0]+1]) rez.a[0]++;
fix(rez.a);
rez.semn=x.semn * y.semn;
return rez;
}
BigInt& BigInt::operator/=(int nr)
{
if (nr<0) semn=-semn, nr=-nr;
ull num=0;
const unsigned k=nr;
for (unsigned i=a[0]; i; i--){
num=a[i] + num*base;
a[i]=num/k;
num%=k;
}
while (!a[a[0]] && a[0]>1) a[0]--;
fix(a);
if (a[0]==1 && !a[1]) semn=0;
return *this;
}
int BigInt::operator%(int nr)
{
ull num=0;
const unsigned k=nr;
for (unsigned i=a[0]; i; i--)
num=(a[i] + num*base)%k;
return num;
}
BigInt operator/(const BigInt &x, const BigInt &y)
{
if (x<y) return 0;
nrdiv+=x.a[0]*y.a[0];
unsigned n=x.a[0], m=y.a[0];
BigInt nr=0, cat, rez;
nr.semn=1; nr.a[0]=0;
nr.a.resize(m+4);
rez.a.resize(n+3);
unsigned i,j;
for (i=n; i>0; i--){
nr.a[0]++;
for (j=nr.a[0]; j>1; j--)
nr.a[j]=nr.a[j-1];
nr.a[1]=x.a[i];
while (nr.a[0]>1 && !nr.a[nr.a[0]]) --nr.a[0];
nr.semn=1;
if (nr<y){ rez.a[i]=0; continue; }
unsigned p,u;
long double num1=(long double) base * nr.a[m+1] + (long double)nr.a[m];
long double num2=(long double) y.a[m];
if (m>1){
num1=num1*base + (long double) nr.a[m-1];
num2=num2*base + (long double) y.a[m-1];
}
if (m==1) p=(unsigned) (num1/num2); else p=(unsigned) (num1/(num2+1));
cat=y;
cat*=p;
u = (unsigned) round((num1+1)/(num2-0.5));
if (m==1) u=(unsigned) round((num1+1)/num2);
if (u>p && cat+y<=nr) cat=cat+y, ++p;
nr=nr-cat;
rez.a[i]=p;
}
while (n>1 && !rez.a[n]) --n;
rez.a[0]=n;
fix(rez.a);
rez.semn=x.semn*y.semn;
return rez;
}
BigInt operator%(const BigInt &x, const BigInt &y)
{
BigInt cat=x/y;
cat=x-(y*cat);
return cat;
}
int operator==(const BigInt &x, const BigInt &y)
{
if (x.semn!=y.semn) return 0;
for (unsigned i=0; i<=y.a[0]; i++)
if (x.a[i]!=y.a[i]) return 0;
return 1;
}
int operator!=(const BigInt &x, const BigInt &y)
{
return !(x == y);
}
int operator<(const BigInt &y, const BigInt &x)
{
if (y.semn < x.semn) return 1;
if (y.semn > x.semn) return 0;
if (y.a[0]<x.a[0]) return 1;
if (y.a[0]>x.a[0]) return 0;
unsigned k=y.a[0];
while (x.a[k]==y.a[k] && k) k--;
int ok=(y.a[k]<x.a[k]);
if (x.semn) return ok; else return !ok;
}
int operator<=(const BigInt &y, const BigInt &x)
{
return ((y<x) || (y==x));
}
int operator>(const BigInt &y, const BigInt &x)
{
return !(y <= x);
}
int operator>=(const BigInt &y, const BigInt &x)
{
return !(y < x);
}
void BigInt::write(FILE *f) const
{
int i,n=a[0];
if (semn==-1) fprintf(f, "-");
fprintf(f, "%u", a[n]);
for (i=n-1; i>0; i--)
fprintf(f, "%.9u", a[i]);
fprintf(f,"\n");
}
void BigInt::read(FILE *f)
{
char c=0;
semn=1;
while (c<'0' || c>'9'){
c=fgetc(f);
if (c=='-') semn=-1;
}
string s="000000000";
while (c>='0' && c<='9') s+=c, c=fgetc(f);
int i, j, n=s.length()/9, lung=s.length()%9;
a.resize(n+2);
if (!lung) lung=9, n--;
for (i=1; i<=n; i++)
for (j=lung; j<lung+9; j++)
a[i]=a[i]*10 + (s[(n-i)*9+j]-'0');
a[0]=n;
while (!a[a[0]] && a[0]>0) a[0]--;
fix(a);
if (a[0]==1 && a[1]==0) semn=0;
}
BigInt pow(const BigInt &a, unsigned nr)
{
BigInt rez=1;
for (unsigned p=(1<<23); p>0; p/=2){
rez=rez*rez;
if (nr&p) rez=rez*a;
}
return rez;
}
BigInt fibo(unsigned n)
{
BigInt a=1, b=1, f1, f3;
unsigned p=1<<22, k=0;
while (p>n) p/=2;
p/=2; k=2;
if (p && (n&p)) b=2, ++k;
for (p/=2; p>1; p/=2){
a=a*a;
b=b*b;
f3=4*b-a;
if (k&1) f3.a[1]-=2; else f3.a[1]+=2;
k*=2;
if (n&p) k++;
f1=a+b;
if (n&p) b=f3, a=f3-f1;
else b=f3-f1, a=f1;
}
if (p){
if (n&1){
b = b+b;
b = (b+a)*(b-a);
if (k&1) b.a[1]-=2; else b.a[1]+=2;
} else b=b*(b+a+a);
}
return b;
}
vector <unsigned> binar(BigInt a)
{
vector <unsigned> rez;
double p=ceil(log(base)/log((double)(1ll<<32))*a.a[0]);
rez.resize((unsigned)p+1);
unsigned nr=0;
while (a.a[0]>1 || a.a[1]>0){
unsigned rest=a%(1<<29);
rez[nr/32]|=rest<<(nr%32);
if (nr%32) rez[nr/32+1]|=rest>>(32-nr%32);
a/=(1<<29);
nr+=29;
}
while (rez.size() && rez[rez.size()-1]==0) rez.resize(rez.size()-1);
return rez;
}
int miller(const BigInt &p, unsigned a)
{
BigInt d=1, x=1, pm=p-1, eg;
vector <unsigned> pow=binar(pm);
unsigned mask=1u<<31;
int nr=pow.size()-1;
while (nr>=0 && (pow[nr] & mask)==0){
mask/=2;
if (!mask) mask=1u<<31, --nr;
}
printf("Biti: %d\n", nr*32+(int) log2(mask));
while (nr>=0){
unsigned op=pow[nr] & mask;
x=d;
if (op) d=(d*d*a)%p; else d=(d*d)%p;
if (op) eg=a; else eg=1;
if (d==eg && x!=pm && x!=1) return 0;
mask/=2;
if (!mask) mask=1u<<31, --nr;
}
return (d==1);
}
int IsPrime(const BigInt &p)
{
unsigned i, primes[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79,
83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
179, 181, 191, 193, 197, 199, 211, 223, 227, 229};
unsigned nr = sizeof(primes)/4;
for (i=0; i<nr; i++){
if (p < primes[i]*primes[i]) return 1;
if (p%primes[i]==0) return 0;
}
for (i=0; i<3; i++) //depinde cat de sigur se vrea, asta e de ajuns in general
if (!miller(p, primes[i])) return 0;
return 1;
}
BigInt gcd(BigInt a, BigInt b)
{
BigInt rest;
while (b!=0){
rest=a%b;
a=b;
b=rest;
}
return a;
}
BigInt extended_gcd(BigInt a, BigInt b, BigInt &x, BigInt &y)
{
x=1; y=0;
BigInt cat, temp, x2=0, y2=1;
while (b!=0){
cat=a/b;
temp=a%b;
a=b; b=temp;
temp=x2;
x2=x-(cat*x2);
x=temp;
temp=y2;
y2=y-(cat*y2);
y=temp;
}
return a;
}
int main()
{
freopen("numere2.in", "r", stdin);
freopen("numere2.out", "w", stdout);
int ord;
BigInt n, SQR, P, i=15999, doi = 2, def;
n.read(stdin);
#define calc(X,Y) \
for(ord = X;ord>Y;--ord)\
{\
i = def;\
SQR = 0;\
while(i.a[0]>1 || i.a[1]>0)\
{\
do\
{\
SQR = SQR + i;\
P = pow(SQR,ord);\
} while(P < n);\
if(n < P)\
SQR = SQR - i;\
i=i/2;\
}\
if(P == n)\
{\
SQR.write(stdout);\
printf("%d\n",ord);\
return 0;\
}\
}
def = 4;
calc(350,200);
def = 11;
calc(199,150);
def = 9999;
calc(149,0);
n.write(stdout);
printf("\n1\n");
return 0;
}