#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <stdint.h>
#include <string>
class BigInt {
public:
explicit BigInt(uint64_t x = 0) {
m_len = 10;
memset(m_cif, 0, sizeof(m_cif));
for (uint32_t i = 0; x; ++i) {
m_cif[i] = x % sm_base;
x /= sm_base;
}
fix();
}
explicit BigInt(const std::string& number) {
const char* digits = number.c_str();
m_len = 0;
memset(m_cif, 0, sizeof(m_cif));
char buff[5];
int poz = strlen(digits) - 4;
while (poz >= 0) {
memset(buff, 0, sizeof(buff));
strncpy(buff, digits + poz, 4);
m_cif[m_len++] = atoi(buff);
poz -= 4;
}
memset(buff, 0, sizeof(buff));
strncpy(buff, digits, 4 + poz);
m_cif[m_len++] = atoi(buff);
fix();
}
BigInt& operator*=(uint32_t scalar) {
for (int i = m_len - 1; i >= 0; --i) {
uint64_t temp = ((uint64_t)m_cif[i]) * ((uint64_t)scalar);
m_cif[i + 2] += (temp / sm_base) / sm_base;
m_cif[i + 1] += (temp / sm_base) % sm_base;
m_cif[i] = temp % sm_base;
}
m_len += 2;
fix();
return *this;
}
BigInt& operator+=(const BigInt& other) {
for (uint32_t i = 0; i < other.m_len; ++i)
m_cif[i] += other.m_cif[i];
m_len = std::max(m_len, other.m_len);
fix();
return *this;
}
BigInt& operator+=(long long other) {
m_cif[0] += other;
fix();
return *this;
}
BigInt operator*(const BigInt& other) {
BigInt result(0);
for (uint32_t i = 0; i < m_len; ++i)
for (uint32_t j = 0; j < other.m_len; ++j) {
result.m_cif[i + j] += m_cif[i] * other.m_cif[j];
result.m_cif[i + j + 1] += result.m_cif[i + j] / sm_base;
result.m_cif[i + j] %= sm_base;
}
result.m_len = m_len + other.m_len;
result.fix();
return result;
}
BigInt& operator/=(unsigned long div) {
long long num = 0;
for (int i = m_len - 1; i >= 0; --i) {
num *= sm_base;
num += m_cif[i];
m_cif[i] = num / div;
num %= div;
}
return *this;
}
bool operator<(const BigInt& other) { return compare(other) < 0; }
bool operator<=(const BigInt& other) { return compare(other) <= 0; }
bool operator>(const BigInt& other) { return compare(other) > 0; }
bool operator>=(const BigInt& other) { return compare(other) >= 0; }
bool operator==(const BigInt& other) { return compare(other) == 0; }
BigInt operator+(const BigInt& other) {
BigInt result(0);
result.m_len = m_len;
memcpy(&result.m_cif, &m_cif, sizeof(m_cif));
result += other;
return result;
}
BigInt operator+(long long other) {
BigInt result(0);
result.m_len = m_len;
memcpy(&result.m_cif, &m_cif, sizeof(m_cif));
result += other;
return result;
}
void print(std::string& output) {
fix();
if (!m_len) { output = "0"; return; }
output.clear();
add_digit(m_cif[m_len - 1], false, output);
for (int i = m_len - 2; i >= 0; --i)
add_digit(m_cif[i], true, output);
}
void raw_print() {
fix();
printf("%lu :", (unsigned long)m_len);
for (int i = m_len - 1; i >= 0; --i)
printf(" %lu", (unsigned long)m_cif[i]);
printf("\n");
}
private:
void fix() {
for (int i = 0; i < (signed)m_len; ++i) {
if (m_cif[i] >= sm_base) {
m_cif[i + 1] += m_cif[i] / sm_base;
m_cif[i] %= sm_base;
if (i + 1 == (signed)m_len) ++m_len;
}
if (m_cif[i] < 0) {
int borrow = (-m_cif[i] + sm_base - 1) / sm_base;
m_cif[i] += borrow * sm_base;
m_cif[i + 1] -= borrow;
}
}
while (m_len && m_cif[m_len - 1] == 0) --m_len;
}
void add_digit(uint32_t digit, bool force_len, std::string& str) {
char buffer[128];
sprintf(buffer, force_len ? "%4.4lu" : "%lu", (unsigned long)digit);
str += buffer;
}
int compare(const BigInt& other) {
if (m_len != other.m_len)
return m_len - other.m_len;
for (int i = m_len - 1; i >= 0; --i)
if (m_cif[i] != other.m_cif[i])
return m_cif[i] - other.m_cif[i];
return 0;
}
static const uint32_t sm_base = 10000;
uint32_t m_cif[64], m_len;
};
#define FISIN "numere2.in"
#define FISOUT "numere2.out"
#define MAXPOW 333
int bad_prime[MAXPOW];
BigInt fastExp(BigInt num, int pow, const BigInt& target, bool& too_big) {
if (pow == 0) { return BigInt(1); }
if (pow == 1) { return num; }
BigInt sqrt = fastExp(num, pow / 2, target, too_big);
if (too_big) return BigInt(1);
BigInt temp = sqrt * sqrt;
BigInt result = (pow & 1) ? (temp * num) : temp;
if (result > target) {
too_big = true;
return BigInt(1);
}
return result;
}
void update_en(BigInt& en, const BigInt& target, long pow) {
BigInt alt = target;
for (int i = 1; i < pow; ++i)
alt /= 2;
if (alt < en) en = alt;
}
int main() {
FILE *fin = fopen(FISIN, "rt");
FILE *fout = fopen(FISOUT, "wt");
char buffer[128];
fscanf(fin, "%s", buffer);
BigInt target(buffer);
int power = 1;
BigInt en(target);
for (int i = 2; i < MAXPOW; ++i) {
if (bad_prime[i]) continue;
for (int j = i * 2; j < MAXPOW; j += i)
bad_prime[j] = 1;
update_en(en, target, i);
BigInt st(1);
while (st <= en) {
BigInt mid = st + en;
mid /= 2;
bool too_big = false;
BigInt pow = fastExp(mid, i, target, too_big);
if (!too_big && pow == target) {
power *= i;
target = mid;
en = target;
update_en(en, target, i);
--i;
break;
}
if (too_big || pow > target) {
en = mid + (-1);
} else {
st = mid + 1;
}
}
}
std::string output; target.print(output);
fprintf(fout, "%s\n%d\n", output.c_str(), power);
fclose(fout);
fclose(fin);
return 0;
}