/* https://codeforces.com/blog/entry/82924 */
/* https://loj.ac/s/938329 (whzzt) */
#include "mushrooms.h"
#include <stdlib.h>
#include <string.h>
using namespace std;
typedef vector<int> vi;
int min(int a, int b) { return a < b ? a : b; }
int max(int a, int b) { return a > b ? a : b; }
const int N = 20000, Q = 203, LG = 7; /* LG = floor(log2(Q)) */
unsigned int X = 12345;
int rand_() {
return (X *= 3) >> 1;
}
char **mask[LG]; int *cnt[LG], *hhh[LG], nn[LG], lower[LG], dp[Q + 1], lg_[Q + 1];
int l_;
void sort(int *hh, int l, int r) {
while (l < r) {
int i = l, j = l, k = r, h = hh[l + rand_() % (r - l)], tmp;
while (j < k)
if (cnt[l_][hh[j]] == cnt[l_][h])
j++;
else if (cnt[l_][hh[j]] < cnt[l_][h]) {
tmp = hh[i], hh[i] = hh[j], hh[j] = tmp;
i++, j++;
} else {
k--;
tmp = hh[j], hh[j] = hh[k], hh[k] = tmp;
}
sort(hh, l, i);
l = k;
}
}
void init() {
int n, n_, q, q_, h, h0, h1, i, lg;
for (lg = 0; lg <= LG; lg++) {
q = 1 << lg, nn[lg] = lg == 0 ? 1 : nn[lg - 1] * 2 + q / 2 - 1;
mask[lg] = (char **) malloc(q * sizeof *mask[lg]);
for (h = 0; h < q; h++)
mask[lg][h] = (char *) calloc(nn[lg], sizeof *mask[lg][h]);
cnt[lg] = (int *) malloc(q * sizeof *cnt[lg]);
hhh[lg] = (int *) malloc(q * sizeof *hhh[lg]);
}
cnt[0][0] = 1, mask[0][0][0] = 1, hhh[0][0] = 0;
lower[0] = 3;
for (lg = 0; lg < LG; lg++) {
n = nn[lg], n_ = nn[lg + 1], q = 1 << lg, q_ = 1 << lg + 1;
for (h = 0; h + 1 < q; h++) {
h0 = h << 1 | 0, h1 = h << 1 | 1;
cnt[lg + 1][h0] = cnt[lg][h] + cnt[lg][h];
cnt[lg + 1][h1] = cnt[lg][h] + (n - cnt[lg][h]) + 1;
for (i = 0; i < n; i++) {
mask[lg + 1][h0][i] = mask[lg][h][i], mask[lg + 1][h0][n + i] = mask[lg][h][i];
mask[lg + 1][h1][i] = mask[lg][h][i], mask[lg + 1][h1][n + i] = mask[lg][h][i] ^ 1;
}
mask[lg + 1][h1][n * 2 + h] = 1;
}
h0 = h << 1 | 0, h1 = h << 1 | 1;
cnt[lg + 1][h0] = n_ - n, cnt[lg + 1][h1] = n_;
for (i = 0; i < n; i++) {
mask[lg + 1][h0][i] = 1, mask[lg + 1][h0][n + i] = 0;
mask[lg + 1][h1][i] = 1, mask[lg + 1][h1][n + i] = 1;
}
for (h = 0; h + 1 < q; h++) {
mask[lg + 1][h0][n * 2 + h] = 1;
mask[lg + 1][h1][n * 2 + h] = 1;
}
for (h = 0; h < q_; h++)
hhh[lg + 1][h] = h;
cnt[lg + 1][q_ - 1] -= cnt[lg + 1][q_ - 2];
l_ = lg + 1, sort(hhh[lg + 1], 0, q_);
for (h = 0; h < q_; h++)
lower[lg + 1] = max(lower[lg + 1], cnt[lg + 1][hhh[lg + 1][h]] * 2 + 1 - h);
cnt[lg + 1][q_ - 1] += cnt[lg + 1][q_ - 2];
}
for (lg = 1; lg <= LG; lg++) {
cnt[lg][(1 << lg) - 1] -= cnt[lg][(1 << lg) - 2];
for (i = 0; i < nn[lg]; i++)
mask[lg][(1 << lg) - 1][i] ^= mask[lg][(1 << lg) - 2][i];
}
for (q = 0; q < 3; q++)
dp[q] = q + 1, lg_[q] = -1;
for (q = 2; q <= Q; q++)
for (lg = 0; lg <= LG && (q + (1 << lg)) <= Q; lg++)
if (dp[q] >= lower[lg]) {
n = dp[q] + nn[lg] + (1 << lg);
if (dp[q + (1 << lg)] < n)
dp[q + (1 << lg)] = n, lg_[q + (1 << lg)] = lg;
}
}
vi ii_;
int ii[2][N], kk[2];
int sum(char *msk, int l, int r, int i_) {
int t, i, k, x;
t = kk[0] > kk[1] ? 0 : 1;
ii_.clear(), k = 0;
if (i_ != -1)
ii_.push_back(i_), ii_.push_back(ii[t][k++]);
for (i = l; i < r; i++)
if (i_ == -1 || msk[i - l])
ii_.push_back(i), ii_.push_back(ii[t][k++]);
x = use_machine(ii_);
if (t == 1)
x = k * 2 - 1 - x;
ii[x % 2][kk[x % 2]++] = i_ == -1 ? l : i_;
return x / 2;
}
int ss[N], tt[N];
void solve(int *ss, int lg, int l) {
int i, a, c;
if (lg == 0) {
ii[ss[0]][kk[ss[0]]++] = l;
return;
}
a = ss[(1 << lg) - 2], c = ss[(1 << lg) - 1] - a;
for (i = 0; i + 1 < 1 << lg - 1; i++) {
int i0 = i << 1 | 0, i1 = i << 1 | 1, t;
t = tt[(1 << lg) + i] = (ss[i0] + ss[i1] + c) % 2;
if (t == 1)
a--;
tt[i] = (ss[i0] + ss[i1] - t - c) / 2, tt[(1 << lg - 1) + i] = (ss[i0] - ss[i1] + t + c) / 2;
ii[t][kk[t]++] = l + nn[lg - 1] * 2 + i;
}
tt[(1 << lg - 1) - 1] = a, tt[(1 << lg) - 1] = c;
memcpy(ss, tt, (1 << lg) * sizeof *ss);
solve(ss, lg - 1, l), solve(ss + (1 << lg - 1), lg - 1, l + nn[lg - 1]);
}
void trace(int q) {
int h, h_, i, l, lg;
if (q == 0) {
ii[0][kk[0]++] = 0;
return;
}
if (q <= 2) {
int x;
trace(q - 1);
ii_.resize(2), ii_[0] = 0, ii_[1] = q, x = use_machine(ii_);
ii[x][kk[x]++] = q;
return;
}
lg = lg_[q];
trace(q - (1 << lg));
l = dp[q - (1 << lg)];
for (h = 0; h < 1 << lg; h++) {
h_ = hhh[lg][h];
ss[h_] = sum(mask[lg][h_], l, l + nn[lg], l + nn[lg] + h);
}
if (lg > 0)
ss[(1 << lg) - 1] += ss[(1 << lg) - 2];
solve(ss, lg, l);
}
int count_mushrooms(int n) {
int q_, q, l, r, ans;
init();
for (q_ = 0; q_ <= Q; q_++) {
int n_ = dp[q_];
for (q = 0; q < Q - q_; q++)
n_ += (dp[q_] + q + 1) / 2;
if (n_ >= n)
break;
}
trace(q_);
ans = n;
for (l = dp[q_]; l < n; l = r)
ans -= sum(NULL, l, r = min(l + max(kk[0], kk[1]), n), -1);
ans -= kk[1];
return ans;
}
