Problem:
Score : 400 points

Problem Statement

Snuke has an empty sequence a.

He will perform N operations on this sequence.

In the i-th operation, he chooses an integer j satisfying 1 \leq j \leq i, and insert j at position j in a (the beginning is position 1).

You are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq b_i \leq N

Input

Input is given from Standard Input in the following format:

N
b_1 \dots b_N

Output

If there is no sequence of N operations after which a would be equal to b, print -1.
If there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.

Sample Input 1

3
1 2 1

Sample Output 1

1
1
2

In this sequence of operations, the sequence a changes as follows:

After the first operation: (1)

After the second operation: (1,1)

After the third operation: (1,2,1)

Sample Input 2

2
2 2

Sample Output 2

-1

2 cannot be inserted at the beginning of the sequence, so this is impossible.

Sample Input 3

9
1 1 1 2 2 1 2 3 2

Sample Output 3

1
2
2
3
1
2
2
1
1

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cassert>

#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>

// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
//#include <boost/foreach.hpp>
//#include <boost/range/algorithm.hpp>
#define rep(i,j,k) for(int i=(int)j;i<(int)k;i++)
#define ll long long
#define Sort(v) sort(all(v))
#define INF 1e9
#define LINF 1e18
#define END return 0
#define pb push_back
#define se second
#define fi first
#define pb push_back
#define all(v) (v).begin() , (v).end()
#define MP make_pair
#define MOD 1000000007LL
#define int long long
using namespace std;
int day[12]={31,28,31,30,31,30,31,31,30,31,30,31};
int dx[]={0,1,0,-1};
int dy[]={1,0,-1,0};
struct edge{int to,cost;};
typedef pair<int,int> P;

bool isupper(char c){if('A'<=c&&c<='Z')return 1;return 0;}
bool islower(char c){if('a'<=c&&c<='z')return 1;return 0;}
bool isPrime(int x){if(x==1)return 0;if(x==2)return 1;if(x%2==0)return 0;for(int i=3;i*i<=x;i++)if(x%i==0)return 0;return 1;}
bool iskaibun(string s){for(int i=0;i<s.size()/2;i++)if(s[i]!=s[s.size()-i-1])return 0;return 1;}
bool isnumber(char c){return ('0'<=c&&c<='9');}
bool isalpha(char c){return (isupper(c)&&islower(c));}
void print(vector<int> v){rep(i,0,v.size()){if(i)cout<<" ";cout<<v[i];}cout<<endl;}
void printl(vector<int> v){rep(i,0,v.size()){cout<<v[i]<<endl;}}

signed main (){
    int n;cin>>n;
    vector<int> v(n);
    rep(i,0,n)cin>>v[i];
    vector<int> ans;
    while(!v.empty()){
        //print(v);
        int ind=-1;
        rep(i,0,v.size()){
            if(v[i]==i+1)ind=i;
        }
        if(ind==-1){
            cout<<-1<<endl;
            return 0;
        }
        ans.push_back(v[ind]);
        v.erase(v.begin()+ind);
    }
    reverse(all(ans));
    printl(ans);
}

/*

*/