#include <algorithm>
#include <fstream>
#include <iostream>
#include <vector>
#include <cstring>
#define NUM_DIGITS 8
using namespace std;
template<class S, class T, class U>
struct triple {
S first;
T second;
U third;
triple(S first, T second, U third) :
first(first), second(second), third(third) { }
bool operator< (triple &other) {
if (first > other.first)
return true;
if (first == other.first) {
if (second > other.second)
return true;
if (second == other.second)
return third > other.third;
}
return false;
}
};
struct bignum {
unsigned int digits[NUM_DIGITS];
bignum()
{
memset(digits, 0, sizeof(digits));
}
bignum(unsigned int value)
{
memset(digits + 1, 0, sizeof(digits) - sizeof(*digits));
digits[0] = value;
}
bool operator== (const bignum &rhs) const
{
return memcmp(digits, rhs.digits, sizeof(digits)) == 0;
}
bool operator!= (const bignum &rhs) const
{
return !(*this == rhs);
}
bool operator< (const bignum &rhs) const
{
for (int i = NUM_DIGITS - 1; i >= 0; i--) {
unsigned int left_digit = digits[i];
unsigned int right_digit = rhs.digits[i];
if (left_digit != right_digit)
return left_digit < right_digit;
}
return false;
}
bignum & operator*= (unsigned int rhs)
{
const unsigned int mask = 0;
unsigned int carry = 0;
for (int i = 0; i < NUM_DIGITS; i++) {
unsigned long long value = digits[i];
value *= rhs;
value += carry;
digits[i] = value & ~mask;
carry = value >> 32;
}
return *this;
}
const pair<bignum, unsigned int> divmod(unsigned int rhs) const
{
const unsigned int mask = 0;
bignum quotient;
unsigned int carry = 0;
int i = NUM_DIGITS - 1;
while (i >= 0 && digits[i] == 0)
i--;
for (; i >= 0; i--) {
unsigned long long value = carry;
value = (value << 32) | digits[i];
unsigned long long q = value / rhs;
quotient.digits[i] = q & ~mask;
carry = value - q * rhs;
}
return pair<bignum, unsigned int>(quotient, carry);
}
friend ostream & operator<< (ostream &os, const bignum &number);
};
const int 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, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359,
367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433,
439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593,
599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743,
751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827,
829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997,
1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163,
1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249,
1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321,
1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439,
1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601,
1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693,
1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783,
1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877,
1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069,
2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143,
2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347,
2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543,
2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657,
2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713,
2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801,
2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011,
3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119,
3121, 3137, 3163,
};
ostream & operator<< (ostream &os, const bignum &number)
{
int i = NUM_DIGITS - 1;
while (i > 0 && number.digits[i] == 0)
i--;
for (; i >= 0; i--) {
cout << number.digits[i];
if (i > 0)
cout << ',';
}
return os;
}
int read_input(const char *filename)
{
int n;
ifstream f(filename);
f >> n;
f.close();
return n;
}
void write_output(const char *filename, const vector<int> &result, int n)
{
ofstream f(filename);
for (vector<int>::const_iterator it = result.begin(); it != result.end(); ++it) {
if (it != result.begin())
f << ' ';
f << n * (*it);
}
f << endl;
f.close();
}
int get_smallest_prime_divisor(int n)
{
size_t num_primes = sizeof(primes) / sizeof(*primes);
for (size_t i = 0; i < num_primes; i++) {
int prime = primes[i];
if (n % prime == 0)
return prime;
}
return 1;
}
int get_largest_exponent(int n, int p)
{
int m = 0;
while (n > 0) {
n /= p;
m++;
}
return m;
}
void find_largest_lcm(int n, vector<int> &result)
{
vector< pair<bignum, int> > a, b;
vector< pair<bignum, int> > &prev = a, &next = b;
size_t num_primes = sizeof(primes) / sizeof(*primes);
prev.push_back(pair<bignum, int>(1, 0));
for (size_t i = 0; i < num_primes; i++) {
next.clear();
int prime = primes[i];
if (prime > n)
break;
int k = get_largest_exponent(n, prime);
vector<int> powers;
int prod = 1;
for (int i = 0; i < k; i++) {
powers.push_back(prod);
prod *= prime;
}
vector< triple<pair<bignum, int>, size_t, int> > v;
pair<bignum, int> primordial = prev.front();
for (int i = 0; i < k; i++) {
int term = powers[i];
pair<bignum, int> adjusted = primordial;
adjusted.first *= term;
if (i > 0)
adjusted.second += term;
v.push_back(triple<pair<bignum, int>, size_t, int>(adjusted, (size_t) 0, i));
}
make_heap(v.begin(), v.end());
while (!v.empty()) {
pop_heap(v.begin(), v.end());
triple<pair<bignum, int>, size_t, int> elem = v.back();
v.pop_back();
pair<bignum, int> candidate = elem.first;
while (!next.empty()) {
pair<bignum, int> last_pair = next.back();
if (last_pair.second >= candidate.second)
next.pop_back();
else
break;
}
next.push_back(candidate);
size_t index = elem.second + 1;
if (index < prev.size()) {
int p_exp = elem.third;
pair<bignum, int> next_pair = prev[index];
if (p_exp > 0)
next_pair.second += powers[p_exp];
if (next_pair.second <= n) {
next_pair.first *= powers[p_exp];
v.push_back(triple<pair<bignum, int>, size_t, int>(next_pair, index, p_exp));
push_heap(v.begin(), v.end());
}
}
}
swap(prev, next);
/*
cout << "p=" << prime << " - k=" << k << " ; " << endl;
for (vector< pair<bignum, int> >::iterator i = prev.begin(); i != prev.end(); ++i) {
cout << i->first << ' ' << i->second << endl;
}
cout << endl;
*/
}
pair<bignum, int> &answer = prev.back();
if (answer.first == answer.second) {
prev.pop_back();
answer = prev.back();
}
bignum factor = answer.first;
int sum = n;
for (size_t i = 0; i < num_primes && factor != 1; i++) {
int prod = 1;
int prime = primes[i];
while (true) {
pair<bignum, unsigned int> qr = factor.divmod(prime);
if (qr.second == 0) {
prod *= prime;
factor = qr.first;
} else {
sum -= prod;
result.push_back(prod);
break;
}
}
}
for (int i = 0; i < sum; i++)
result.push_back(1);
}
int main()
{
vector<int> result;
int n, p;
n = read_input("nummst.in");
p = get_smallest_prime_divisor(n);
find_largest_lcm(p, result);
write_output("nummst.out", result, n / p);
return 0;
}