This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define EmiliaMyWife ios::sync_with_stdio(0); cin.tie(0);
using ll = int64_t;
using uint = uint32_t;
using ull = uint64_t;
using ld = long double;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
const double EPS = 1e-8;
const ll LINF = ll(1e18) + ll(1e15);
static auto LamyIsCute = []() {
EmiliaMyWife
return 48763;
}();
signed main() {
int n;
cin >> n;
if(n == 0) {
cout << "0\n";
return 0;
}
n = 1 << n;
vector<int> arr(n);
for(int i = 0; i < n; i++)
cin >> arr[i];
map<vector<int>, int> has;
has[arr] = 0;
queue<vector<int>> bfs;
bfs.push(arr);
while(!bfs.empty()) {
auto a = bfs.front();
bfs.pop();
auto b = a;
for(int i = 0; i < n; i++) {
if(i & 1)
b[i / 2 + n / 2] = a[i];
else
b[i / 2] = a[i];
}
for(int i = 0; i < n / 2; i++)
swap(a[i], a[i + n / 2]);
if(!has.count(b)) {
has[b] = 2;
bfs.push(b);
}
if(!has.count(a)) {
has[a] = 1;
bfs.push(a);
}
}
auto rev = [&](const vector<int> &arr) {
int res = 0;
for(int i = 0; i < n; i++)
for(int j = 0; j < i; j++)
res += arr[j] > arr[i];
return res;
};
vector<int> ans;
int w = INF;
for(const auto &[a, b] : has) {
int x = rev(a);
if(x < w)
w = x, ans = a;
}
cout << w << '\n';
string s;
vector<int> tmp(n);
while(has[ans]) {
//for(int x : ans)
//cout << x << ' ';
//cout << '\n';
if(has[ans] == 1) {
for(int i = 0; i < n / 2; i++)
swap(ans[i], ans[i + n / 2]);
s += '1';
}
else {
for(int i = 0; i < n; i += 2)
tmp[i] = ans[i / 2];
for(int i = 1; i < n; i += 2)
tmp[i] = ans[i / 2 + n / 2];
ans = tmp;
s += '2';
}
}
reverse(s.begin(), s.end());
cout << s << '\n';
}
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