Language: C++

#include <iostream>
#include <cstdio>
#include <vector>
#define _USE_MATH_DEFINES
#include <math.h>
#include <cstring>
#include <numeric>
#include <algorithm>
#include <stdlib.h>
#include <functional>
#include <string>
#include <array>
#include <map>
#include <queue>
#include <limits.h>
#include <set>
#include <stack>
#include <random>
#include <complex>
#include <unordered_map>
#include <nmmintrin.h>
#include <chrono>
#define rep(i,s,n) for(int i = (s); (n) > i; i++)
#define REP(i,n) rep(i,0,n)
#define RANGE(x,a,b) ((a) <= (x) && (x) <= (b))
#define DUPLE(a,b,c,d) (RANGE(a,c,d) || RANGE(b,c,d) || RANGE(c,a,b) || RANGE(d,a,b))
#define INCLU(a,b,c,d) (RANGE(a,c,d) && (b,c,d))
#define PW(x) ((x)*(x))
#define ALL(x) (x).begin(), (x).end()
#define MODU 1000000007
#define bitcheck(a,b)   ((a >> b) & 1)
#define bitset(a,b)      ( a |= (1 << b))
#define bitunset(a,b)    (a &= ~(1 << b))
#define MP(a,b) make_pair((a),(b))
#define Manh(a,b) (abs((a).first-(b).first) + abs((a).second - ((b).second))
#define pritnf printf
#define scnaf scanf
#define itn int

using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
ll gcd(ll a, ll b) {
	if (b == 0) return a;
	return gcd(b, a%b);
}
template<typename A, size_t N, typename T>
void Fill(A(&array)[N], const T &val) {
	std::fill((T*)array, (T*)(array + N), val);
}

class Bitvector {
	//4byteブロック 全部半径、0-index
	static const int mask[32];
public:

	unsigned int* st;
	unsigned int* blockrank;
	int sz;
	Bitvector(int n) {
		sz = n;
		st = (unsigned int*)calloc((n + 31) / 32, sizeof(int));
		blockrank = (unsigned int*)calloc((n + 31) / 32 + 1, sizeof(int));
		if (st == NULL || blockrank == NULL)
			abort();
	}
	inline void set(int a, bool f) {//後から追加はできない
		if (f)bitset(st[a / 32], (31 - a % 32));
	}
	inline bool get(int a) { return bitcheck(st[a / 32], (31 - a % 32)); }
	inline void calcblock() {
		int cou = 0;
		REP(i, sz + 1) {
			if (i && !(i % 32))blockrank[i / 32] = cou;
			if (i<sz)cou += bitcheck(st[i / 32], (31 - i % 32));
		}
	}
	int rank(int a, bool t) {
		int ret = blockrank[a / 32] + (((32 - a % 32) >= 32) ? 0 : _mm_popcnt_u32(st[a / 32] >> (32 - a % 32)));
		return t ? ret : a - ret;
	}
	int select(int a, bool t) {
		int l = 0, r = sz + 1;

		while (r - l > 1) {
			int mid = (l + r) / 2;
			if (rank(mid, t) >= a) r = mid;
			else l = mid;
		}
		if (rank(r, t) < a) return -1;
		return r;
	}
	void clear() {
		free(st);
		free(blockrank);
	}
};

//プリミティブ型だけだよ！！！！(低レベルでうぇぶるので)
template<typename T>
class WaveletMatrix {
public:
	vector<T> data;
	vector<Bitvector> bitv;
	vector<int> border;
	int bitsize;
	WaveletMatrix(vector<T>& dat) : bitsize(sizeof(T) * 8), data(dat) {
		bitv.reserve(bitsize);
		REP(i, bitsize + 1)
			bitv.push_back(Bitvector(data.size()));
		border.resize(bitsize + 1);
		REP(j, data.size())
			bitv[0].set(j, bitcheck(data[j], bitsize - 1));
		bitv[0].calcblock();
		vector<T> buf[2];
		buf[0] = data;
		buf[1].resize(data.size());

		REP(i, bitsize - 1) {
			border[i + 1] = bitv[i].rank(data.size(), 0);
			int cou[2] = { 0, border[i + 1] };
			REP(j, data.size()) {
				bitv[i + 1].set(cou[bitv[i].get(j)], bitcheck(buf[i % 2][j], bitsize - i - 2));
				buf[1 - i % 2][cou[bitv[i].get(j)]] = buf[i % 2][j] << (i + 1) >> (i + 1);
				cou[bitv[i].get(j)]++;
			}
			bitv[i + 1].calcblock();
		}
		border[bitsize] = bitv[bitsize - 1].rank(data.size(), 0);
	}

	pii search(int s, int e, unsigned int t, int b = 0) {
		if (b == bitsize) return{ s,e };
		bool cur = bitcheck(t, bitsize - 1);
		return search(cur*border[b + 1] + bitv[b].rank(s, cur), cur*border[b + 1] + bitv[b].rank(e, cur), t << 1, b + 1);
	}
	int backward(int a, unsigned int t, int b = 0) {
		if (b == bitsize - 1) return a;
		backward(bitv[bitsize - b - 1].select(a + 1 - bitcheck(t, 0) * border[bitsize - b], bitcheck(t, 0)) - 1, t >> 1, b + 1);
	}

	int rank(int s, int e, T t) {
		pii r = search(s, e, t);
		return r.second - r.first;
	}

	int select(int a, T t) {
		pii r = search(0, data.size(), t);
		return  backward(r.first + a - 1, t);
	}

	T kthelement(int s, int e, int k, int b = 0) {
		int eo = bitv[b].rank(e, 0), so = bitv[b].rank(s, 0), cou = eo - so;
		if (b == bitsize - 1) return cou <= k;
		return (cou <= k ?
			kthelement(border[b + 1] + (s - so), border[b + 1] + (s - so) + (e - s - cou), k - cou, b + 1) :
			kthelement(so, so + cou, k, b + 1)) | ((cou <= k) << (bitsize - b - 1));
	}
	int less(int s, int e, T t, int b = 0) {
		int eo = bitv[b].rank(e, 0), so = bitv[b].rank(s, 0), cou = (eo - so);
		if (b == bitsize) return e - s;
		return bitcheck(t, bitsize - b - 1) ?
			less(border[b + 1] + (s - so), border[b + 1] + (s - so) + (e - s - cou), t, b + 1) + cou :
			less(so, so + cou, t, b + 1);
	}

	~WaveletMatrix() {
		REP(i, bitsize) bitv[i].clear();
	}
};

signed main() {
	int n;
	cin >> n;
	vector<int> num[2];
	num[0].resize(n / 2);
	num[1].resize(n / 2);
	REP(i, n) {
		scanf("%d", &num[i%2][i/2]);
	}
	WaveletMatrix<int> *wm[2];

	wm[0] = new WaveletMatrix<int>(num[0]);
	wm[1] = new WaveletMatrix<int>(num[1]);

	queue<pii> cc;
	cc.push({ 0,n });

	priority_queue<pair<pii, pair<pii,pii>>, vector<pair<pii, pair<pii, pii>>>, greater<pair<pii, pair<pii, pii>>>> pq;
	do {
		while (cc.size()) {
			pii ck = cc.front();
			cc.pop();

			bool turn = ck.first % 2;

			int cur = wm[turn]->kthelement(ck.first / 2, (ck.second + !turn) / 2, 0);

			int br = wm[turn]->rank(0, ck.first / 2, cur);
			int pos = wm[turn]->select(br + 1, cur);
			pos = pos * 2 + turn;

			int aik = wm[!turn]->kthelement((pos + 1) / 2, (ck.second + turn) / 2, 0);

			int br2 = wm[!turn]->rank(0, (pos + turn) / 2, aik);
			int apos = wm[!turn]->select(br2 + 1, aik);
			apos = apos * 2 + !turn;

			pq.push({ {cur,aik}, {ck, {pos,apos} } });
		}

		auto top = pq.top();
		pq.pop();
		pii ck = top.second.first;
		int pos = top.second.second.first, apos = top.second.second.second;
		if (ck.first != pos)
			cc.push({ ck.first, pos });
		if (pos + 1 != apos)
			cc.push({ pos + 1 , apos });
		if (apos + 1 != ck.second)
			cc.push({ apos + 1, ck.second });

		printf("%d %d ", top.first.first, top.first.second);

	} while (cc.size() || pq.size());

	return 0;
}

Compiler output:
a.cc: In member function 'int WaveletMatrix<T>::backward(int, unsigned int, int) [with T = int]':
a.cc:140:25: warning: control reaches end of non-void function [-Wreturn-type]
  140 |                 backward(bitv[bitsize - b - 1].select(a + 1 - bitcheck(t, 0) * border[bitsize - b], bitcheck(t, 0)) - 1, t >> 1, b + 1);
      |                 ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/lib/gcc/x86_64-linux-gnu/14/include/smmintrin.h:812,
                 from /usr/lib/gcc/x86_64-linux-gnu/14/include/nmmintrin.h:31,
                 from a.cc:21:
/usr/lib/gcc/x86_64-linux-gnu/14/include/popcntintrin.h: In member function 'int Bitvector::rank(int, bool)':
/usr/lib/gcc/x86_64-linux-gnu/14/include/popcntintrin.h:35:1: error: inlining failed in call to 'always_inline' 'int _mm_popcnt_u32(unsigned int)': target specific option mismatch
   35 | _mm_popcnt_u32 (unsigned int __X)
      | ^~~~~~~~~~~~~~
a.cc:80:90: note: called from here
   80 |                 int ret = blockrank[a / 32] + (((32 - a % 32) >= 32) ? 0 : _mm_popcnt_u32(st[a / 32] >> (32 - a % 32)));
      |                                                                            ~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~