## 453B

Posted on 06 Dec 2014

### Solution

#include <cstdio>
#include <cmath>
#include <algorithm>
#include <cstring>
using namespace std;

#define D(x)

const int MAX_N = 120;
const int MAX_A = 65;
const int INF = 0x3f3f3f3f;

int seq_a[MAX_N];
int seq_b[MAX_N];
int f[MAX_N][1 << 18];
int path[MAX_N][1 << 18];
int prime[20];
int factor_bits[MAX_A];
int num;
int n;

bool is_prime(int a)
{
for (int i = 2; i <= a / 2; i++)
{
if (a % i == 0)
{
return false;
}
}
return true;
}

int make_factor(int a)
{
int ret = 0;
for (int i = 0; i < num; i++)
{
ret <<= 1;
if (a % prime[i] == 0)
{
ret = ret | 1;
}
}
return ret;
}

void init()
{
num = 0;
for (int i = 2; i <= 60; i++)
{
if (is_prime(i))
{
prime[num++] = i;
}
}
for (int i = 1; i < 60; i++)
{
factor_bits[i] = make_factor(i);
}
}

void input()
{
scanf("%d", &n);
for (int i = 1; i <= n; i++)
{
scanf("%d", &seq_a[i]);
}
}

void work()
{
memset(f, -1, sizeof(f));
f[0][0] = 0;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < (1 << num); j++)
{
if (f[i][j] == -1)
continue;
for (int k = 1; k < 60; k++)
{
if ((j & factor_bits[k]) != 0)
continue;
if (f[i + 1][j | factor_bits[k]] == -1 || f[i + 1][j | factor_bits[k]] > f[i][j] + abs(seq_a[i + 1] - k))
{
f[i + 1][j | factor_bits[k]] = f[i][j] + abs(seq_a[i + 1] - k);
path[i + 1][j | factor_bits[k]] = k;
}
}
}
}
int ans = INF;
int temp;
for (int i = 0; i < (1 << num); i++)
{
if (f[n][i] == -1)
continue;
if (ans > f[n][i])
{
ans = f[n][i];
temp = i;
}
}
for (int i = n; i > 0; i--)
{
seq_b[i] = path[i][temp];
temp -= factor_bits[path[i][temp]];
}

for (int i = 1; i <= n; i++)
{
if (i != 1)
putchar(' ');
printf("%d", seq_b[i]);
}
}

int main()
{
init();
input();
work();
return 0;
}