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 <string>
#include <vector>
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<stack>
#include<queue>
#include<cmath>
#include<algorithm>
#include<functional>
#include<list>
#include<deque>
#include<bitset>
#include<set>
#include<map>
#include<unordered_map>
#include<unordered_set>
#include<cstring>
#include<sstream>
#include<complex>
#include<iomanip>
#include<numeric>
#include<cassert>
#define X first
#define Y second
#define pb push_back
#define rep(X,Y) for (int (X) = 0;(X) < (Y);++(X))
#define reps(X,S,Y) for (int (X) = S;(X) < (Y);++(X))
#define rrep(X,Y) for (int (X) = (Y)-1;(X) >=0;--(X))
#define rreps(X,S,Y) for (int (X) = (Y)-1;(X) >= (S);--(X))
#define repe(X,Y) for ((X) = 0;(X) < (Y);++(X))
#define peat(X,Y) for (;(X) < (Y);++(X))
#define all(X) (X).begin(),(X).end()
#define rall(X) (X).rbegin(),(X).rend()
#define eb emplace_back
#define UNIQUE(X) (X).erase(unique(all(X)),(X).end())
#define Endl endl

using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
template<class T> using vv=vector<vector<T>>;
template<class T> ostream& operator<<(ostream &os, const deque<T> &t) {
os<<"{"; rep(i,t.size()) {os<<t[i]<<",";} os<<"}"<<endl; return os;}
template<class T> ostream& operator<<(ostream &os, const vector<T> &t) {
os<<"{"; rep(i,t.size()) {os<<t[i]<<",";} os<<"}"<<endl; return os;}
template<class T,size_t n> ostream& operator<<(ostream &os, const array<T,n> &t) {
	os<<"{"; rep(i,n) {os<<t[i]<<",";} os<<"}"<<endl; return os;}
template<class S, class T> ostream& operator<<(ostream &os, const pair<S,T> &t) { return os<<"("<<t.first<<","<<t.second<<")";}
template<class S, class T,class U> ostream& operator<<(ostream &os, const tuple<S,T,U> &t) { return os<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<")";}
template<class S, class T,class U,class V> ostream& operator<<(ostream &os, const tuple<S,T,U,V> &t) { return os<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<","<<get<3>(t)<<")";}
template<class S, class T,class U,class V,class W> ostream& operator<<(ostream &os, const tuple<S,T,U,V,W> &t) { return os<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<","<<get<3>(t)<<","<<get<4>(t)<<")";}
template<class T> inline bool MX(T &l,const T &r){return l<r?l=r,1:0;}
template<class T> inline bool MN(T &l,const T &r){return l>r?l=r,1:0;}
//#undef NUIP
#ifdef NUIP
#define out(args...){vector<string> a_r_g_s=s_p_l_i_t(#args, ','); e_r_r(a_r_g_s.begin(), args); }
vector<string> s_p_l_i_t(const string &s, char c){vector<string> v;int d=0,f=0;string t;for(char c:s){if(!d&&c==',')v.pb(t),t="";else t+=c;if(c=='\"'||c=='\'')f^=1;if(!f&&c=='(')++d;if(!f&&c==')')--d;}v.pb(t);return move(v);}
void e_r_r(vector<string>::iterator it) {}
template<typename T, typename... Args> void e_r_r(vector<string>::iterator it, T a, Args... args){ if(*it==" 1"||*it=="1") cerr<<endl; else cerr << it -> substr((*it)[0] == ' ', it -> length()) << " = " << a << ", "; e_r_r(++it, args...);}
#else
#define out
#endif
#ifdef __cpp_init_captures
template<typename T>vector<T> table(int n, T v){ return vector<T>(n, v);}
template <class... Args> auto table(int n, Args... args){auto val = table(args...); return vector<decltype(val)>(n, move(val));}
#endif
const ll MOD=1e9+7;

int main(){
  ios_base::sync_with_stdio(false);
  cout<<fixed<<setprecision(0);
	int n;
	cin>>n;
	vector<int> b(n);
	rep(i,n) cin>>b[i], --b[i];
	vector<int> re;
	while(b.size()){
		int k=-1;
		rrep(i,b.size()){
			if(i==b[i]){
				k=i; break;
			}
		}
		if(k<0){
			cout<<-1<<endl;
			return 0;
		}
		re.pb(k);
		b.erase(b.begin()+k);
	}
	reverse(all(re));
	for(int x:re) cout<<x+1<<endl;
  return 0;
}