Problem:
Score : 800 points

Problem Statement

Let N be a positive even number.

We have a permutation of (1, 2, ..., N), p = (p_1, p_2, ..., p_N).
Snuke is constructing another permutation of (1, 2, ..., N), q, following the procedure below.

First, let q be an empty sequence.
Then, perform the following operation until p becomes empty:

Select two adjacent elements in p, and call them x and y in order. Remove x and y from p (reducing the length of p by 2), and insert x and y, preserving the original order, at the beginning of q.

When p becomes empty, q will be a permutation of (1, 2, ..., N).

Find the lexicographically smallest permutation that can be obtained as q.

Constraints

N is an even number.

2 ≤ N ≤ 2 × 10^5

p is a permutation of (1, 2, ..., N).

Input

Input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

Output

Print the lexicographically smallest permutation, with spaces in between.

Sample Input 1

4
3 2 4 1

Sample Output 1

3 1 2 4

The solution above is obtained as follows:

p

q

(3, 2, 4, 1)

()

↓

↓

(3, 1)

(2, 4)

↓

↓

()

(3, 1, 2, 4)

Sample Input 2

2
1 2

Sample Output 2

1 2

Sample Input 3

8
4 6 3 2 8 5 7 1

Sample Output 3

3 1 2 7 4 6 8 5

The solution above is obtained as follows:

p

q

(4, 6, 3, 2, 8, 5, 7, 1)

()

↓

↓

(4, 6, 3, 2, 7, 1)

(8, 5)

↓

↓

(3, 2, 7, 1)

(4, 6, 8, 5)

↓

↓

(3, 1)

(2, 7, 4, 6, 8, 5)

↓

↓

()

(3, 1, 2, 7, 4, 6, 8, 5)

Solution in C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

//set many funcs template
//Ver.20181228
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<time.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384
#define size 524288

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int nHr(int a,int b){return nCr(a+b-1,b);}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
int dsum(int x){int r=0;while(x){r+=(x%10);x/=10;}return r;}
int dsumb(int x,int b){int r=0;while(x){r+=(x%b);x/=b;}return r;}
int sankaku(int x){return ((1+x)*x)/2;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llnHr(long long a,long long b){return llnCr(a+b-1,b);}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long lldsum(long long x){long long r=0;while(x){r+=(x%10);x/=10;}return r;}
long long lldsumb(long long x,long long b){long long r=0;while(x){r+=(x%b);x/=b;}return r;}
long long llsankaku(long long x){return ((1+x)*x)/2;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int strsortfncsj(const void *a,const void *b){return strcmp((char *)a,(char *)b);}
int strsortfnckj(const void *a,const void *b){return strcmp((char *)b,(char *)a);}
int chsortfncsj(const void *a,const void *b){if(*(char *)a>*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}
int chsortfnckj(const void *a,const void *b){if(*(char *)a<*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}

void shuffledget(int x[],int n){
    srand(time(0));
    int i,b[524288],p,c;
    for(i=0;i<n;i++){
        b[i]=i;
    }
    for(i=n;i>=1;i--){
        p=rand()%i;
        c=b[i-1];b[i-1]=b[p];b[p]=c;
    }
    for(i=0;i<n;i++){
        scanf("%d",&x[b[i]]);
    }
}

int dx4[4]={1,-1,0,0};
int dy4[4]={0,0,1,-1};
int dx8[8]={-1,-1,-1,0,0,1,1,1};
int dy8[8]={-1,0,1,-1,1,-1,0,1};

int search(int x,int a[],int n){
    int st=0,fi=n-1,te;
    while(st<=fi){
        te=(st+fi)/2;
        if(a[te]<x){st=te+1;}else{fi=te-1;}
    }
    return st;
}

void prarr(long long arr[],long long n){
  long long i;
  for(i=0;i<n;i++){
    if(i){printf(" ");}
    printf("%lld",arr[i]);
  }
  printf("\n");
  return;
}

typedef struct{
long long val;
long long node;
}data;

long long ssize=size;
data vd;

void sinit(data stree[]){
    vd.val=llinf;
    vd.node=-1;
    long long i,j;
    for(i=0;i<2*ssize;i++){
        stree[i].val=llinf;
        stree[i].node=-1;
    }
}

void upd(data stree[],long long k,data a){
    long long i,m;
    data ld,rd,md;
    k+=ssize-1;
    stree[k]=a;
    while(k>0){
        k=(k-1)/2;
        ld=stree[2*k+1];
        rd=stree[2*k+2];
        if(ld.val<rd.val){md=ld;}
        else{md=rd;}
        stree[k]=md;
    }
}

//calc min[a,b)
//call:k=0,l=0,r=ssize
data query(data stree[],long long a,long long b,long long k,long long l,long long r){
    data ld,rd;
    if(r<=a || b<=l){return vd;}
    if(a<=l && r<=b){
        return stree[k];
    }
    else{
        ld=query(stree,a,b,k*2+1,l,(l+r)/2);
        rd=query(stree,a,b,k*2+2,(l+r)/2,r);
        if(ld.val<rd.val){return ld;}
        else{return rd;}
    }
}

long long n;
data seg[2][2*size];
long long res[size];
long long mr[size];

void solve(long long st,long long fi,long long pt){
  if(st>=fi){return;}
  long long i,w,p;
  long long fp,sp,tp,lp;
  data fm,sm;
  w=st%2;
  fm=query(seg[w],st,fi+1,0,0,ssize);
  p=fm.node;
  w=1-w;
  sm=query(seg[w],p+1,fi+1,0,0,ssize);
  res[pt]=fm.val;
  res[pt+1]=sm.val;
  pt+=2;
  fp=pt;
  solve(st,fm.node-1,fp);
  pt+=((fm.node-st));
  sp=pt;
  solve(fm.node+1,sm.node-1,sp);
  pt+=((sm.node-(fm.node+1)));
  tp=pt;
  solve(sm.node+1,fi,tp);
  pt+=(fi-sm.node);
  lp=pt;

  long long nf=fp,ns=sp,nt=tp,c=0,v;
  while(nf<sp || ns<tp || nt<lp){
    v=llinf;
    if(nf<sp){
      if(res[nf]<v){
        v=res[nf];
        w=1;
      }
    }

    if(ns<tp){
      if(res[ns]<v){
        v=res[ns];
        w=2;
      }
    }

    if(nt<lp){
      if(res[nt]<v){
        v=res[nt];
        w=3;
      }
    }

    if(w==1){
      mr[c]=res[nf];
      c++;
      nf++;
      mr[c]=res[nf];
      c++;
      nf++;
    }
    if(w==2){
      mr[c]=res[ns];
      c++;
      ns++;
      mr[c]=res[ns];
      c++;
      ns++;
    }
    if(w==3){
      mr[c]=res[nt];
      c++;
      nt++;
      mr[c]=res[nt];
      c++;
      nt++;
    }
  }
  for(i=0;i<c;i++){
    res[fp]=mr[i];
    fp++;
  }
}

int main(void){
    long long i,j,m,k,a[size],b,c,h,w,r=0,l,t;
    data pd;
    sinit(seg[0]);
    sinit(seg[1]);
    scanf("%lld",&n);
    for(i=0;i<n;i++){
      scanf("%lld",&a[i]);
      if(i%2==0){
        pd.val=a[i];
        pd.node=i;
        upd(seg[0],i,pd);
        pd.val=llinf;
        upd(seg[1],i,pd);
      }
      else{
        pd.val=a[i];
        pd.node=i;
        upd(seg[1],i,pd);
        pd.val=llinf;
        upd(seg[0],i,pd);
      }
    }
    //printf("ok\n");
    solve(0,n-1,0);
    prarr(res,n);
    return 0;
}