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.

Examples

Input

3
1 2 1


Output

1
1
2


Input

2
2 2


Output

-1


Input

9
1 1 1 2 2 1 2 3 2


Output

1
2
2
3
1
2
2
1
1
import java.io.IOException;
import java.io.InputStream;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        int[] b = new int[n];
        for (int i=0;i<n;i++)b[i]=sc.nextInt();
        Stack<Pair<Integer,int[]>> q = new Stack<>();
        q.push(new Pair<>(0,b));
        int count = 0;
        Basic base = new Basic();
        HashMap<Integer,int[]> map = new HashMap<>();
        map.put(0,new int[n]);
        boolean is = false;
        int ansKey = -1;
        while (!q.isEmpty()&&!is){
            Pair VV = q.pop();
            int ins = (int)VV.A;
            int[] v = (int[])VV.B;
            if (v.length==1){
                if (v[0]==1){
                    map.get(ins)[0]=1;
                    is=true;
                    ansKey=ins;
                }
            }else {
                boolean bool = true;
                boolean bb = true;
                for (int i=v.length-1;i>=0&&bb;i--){
                    if (v[i]==i+1){
                        bb=false;
                        int a;
                        if (bool){
                            a=ins;
                            bool=false;
                        }else {
                            count++;
                            a=count;
                        }
                        q.push(new Pair<>(a,base.remove(v,i)));
                        int[] an = map.get(ins).clone();
                        an[v.length-1]=i+1;
                        map.put(a,an);
                    }
                }
            }
        }
        if (is){
            int[] ans = map.get(ansKey);
            for (int i=0;i<n;i++)System.out.println(ans[i]);
        }else System.out.println(-1);
    }

    public long MOD = 1000000007;
    public static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            }else{
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }else if(b == -1 || !isPrintableChar(b)){
                    return minus ? -n : n;
                }else{
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }
        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
    }
    public static class Basic {
        //math
        private final int MAX = 510000;
        private final int MOD = 1000000007;
        private final long[] fac = new long[MAX];
        private final long[] finv= new long[MAX];
        private final long[] inv = new long[MAX];
        public long factorial(long num){
            if (num<2)return 1;
            else return num*factorial(num-1);
        }
        public int arraySum(int[] array){
            int ans = 0;
            for (int value : array) ans += value;
            return ans;
        }
        public double log(double base,double antilogarithm){
            return Math.log(antilogarithm)/Math.log(base);
        }
        public int gcd(int x,int y){
            if (y==0)return x;
            else return gcd(y,x%y);
        }
        public int lcm(int x,int y){
            return x/gcd(x,y)*y;
        }
        public HashMap<Long,Long> factorization(long num){
            HashMap<Long,Long> hash = new HashMap<>();
            long n = num;
            long count = 2;
            while (n>1){
                while (n%count==0){
                    n/=count;
                    if (hash.containsKey(count))hash.put(count,hash.get(count)+1);
                    else hash.put(count,1L);
                }
                count++;
            }
            return hash;
        }
        public int sum(int[] num){
            int ans = 0;
            for (int i = 0; i < num.length;i++){
                ans += num[i];
            }
            return ans;
        }
        public int[] reduce(int small, int big){
            int ins = 2;
            while (ins<=small){
                if (small%ins==0&&big%ins==0){
                    small/=ins;
                    big/=ins;
                    ins = 2;
                }else {
                    ins++;
                }
            }
            return new int[]{small, big};
        }
        public int reduceCount(int small, int big){
            int ins = 2;
            int ans = 0;
            while (ins<=small){
                if (small%ins==0&&big%ins==0){
                    small/=ins;
                    big/=ins;
                    ins = 2;
                    ans++;
                }else {
                    ins++;
                }
            }
            return ans;
        }
        public int binarySearch(int[] array, int target){
            int pos = -1;
            int left = 0;
            int right = array.length-1;
            int middle;
            while (pos==-1&&left<=right){
                middle = (left+right)/2;
                if (array[middle]==target)pos=middle;
                else if (array[middle]>target)right=middle-1;
                else left=middle+1;
            }
            return pos;
        }
        public long modPow(long a, long n, long mod){
            long res = 1;
            while (n>0){
                if ((n&1)!=0)res = res*a%mod;
                a=a*a%mod;
                n >>= 1;
            }
            return res;
        }
        public long modinv(long a, long mod){return modPow(a,mod-2,mod);}
        public void COMinit(){
            fac[0]=1;
            fac[1]=1;
            finv[0]=1;
            finv[1]=1;
            inv[1]=1;
            for (int i=2;i<MAX;i++){
                fac[i]=fac[i-1]*i%MOD;
                inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
                finv[i]=finv[i-1]*inv[i]%MOD;
            }
        }
        public long COM(int n, int k){
            if (n<k)return 0;
            if (n<0||k<0)return 0;
            return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
        }
        public long HCOM(int n, int k){
            return COM(n+k-1,k);
        }

        //array
        public int[] remove(int[] ar,int pos){
            int[] ret = new int[ar.length-1];
            for (int i=0;i<pos;i++)ret[i]=ar[i];
            for (int i=pos+1;i<ar.length;i++)ret[i-1]=ar[i];
            return ret;
        }
    }
    public static class Queue<T>{
        private final int max = 1000000;
        private final T[] queue = (T[]) new Object[max];
        private int tail = 0; private int head = 0;
        public void init(){this.head = 0; tail = 0;}
        public boolean isEmpty(){return (head==tail);}
        public boolean isFull(){return (head == (tail+1)%max);}
        public void enqueue(T v){
            if (isFull()){
                System.out.println("error: queue is full.");
                return;
            }
            queue[tail++] = v;
            if (tail == max) tail = 0;
        }
        public T dequeue(){
            if (isEmpty()){
                System.out.println("error: queue is empty");
                return null;
            }
            T res = queue[head];
            ++head;
            if (head == max) head = 0;
            return res;
        }
    }
    public static class Stack<T>{
        private final int max = 100000;
        private final T[] stack =(T[]) new Object[max];
        private int top = 0;
        public boolean isEmpty(){return (top==0);}
        public boolean isFull(){return (top==max);}
        public void init(){top=0;}
        public void push(T v){
            if (isFull()){
                System.out.println("error: stack is full.");
                return;
            }
            stack[top++] = v;
        }
        public T pop(){
            if (isEmpty()){
                System.out.println("error: stack is empty");
                return null;
            }
            return stack[--top];
        }
    }
    public static class Pair<K,V>{
        private K A;
        private V B;
        Pair(K a,V b){
            A=a;
            B=b;
        }
        public void changeA(K a){A=a;}
        public void changeB(V b){B=b;}
        public void changeAB(K a,V b){A=a;B=b;}
        public static Comparator numberSortWithA = new Comparator() {
            @Override
            public int compare(Object o1, Object o2) {
                Pair p = (Pair)o1;
                Pair q = (Pair)o2;
                if ((int)p.A<(int)q.A)return -1;
                else if ((int)p.A==(int)q.A)return 0;
                else return 1;
            }
        };
        public static Comparator numberSortWithB = new Comparator() {
            @Override
            public int compare(Object o1, Object o2) {
                Pair p = (Pair)o1;
                Pair q = (Pair)o2;
                if ((int)p.B<(int)q.B)return -1;
                else if ((int)p.B==(int)q.B)return 0;
                else return 1;
            }
        };
    }
    public static class Graph{
        private final HashMap<Integer,HashSet<Integer>> graph = new HashMap<>();
        private final int Size;
        private int[] Depth;
        Graph(int size){
            for (int i=0;i<size;i++)graph.put(i,new HashSet<>());
            Size = size;
        }

        public void addEdge(int node1,int node2){
            if (graph.containsKey(node1)&&graph.containsKey(node2)){
                graph.get(node1).add(node2);
                graph.get(node2).add(node1);
            }
        }
        public void addDirectEdge(int from,int to){
            if (graph.containsKey(from)&&graph.containsKey(to)){
                graph.get(from).add(to);
            }
        }
        public int[] Depth(int root){
            Queue<Integer> q = new Queue<>();
            q.enqueue(root);
            boolean[] seen = new boolean[Size];
            Arrays.fill(seen, false);
            seen[root]=true;
            int[] depth = new int[Size];
            depth[root]=0;
            while (!q.isEmpty()){
                int v = q.dequeue();
                for (int u : graph.get(v)){
                    if (!seen[u]){
                        seen[u]=true;
                        q.enqueue(u);
                        depth[u]=depth[v]+1;
                    }
                }
            }
            Depth = depth.clone();
            return depth;
        }
    }
    public static class UnionFindTree{
        int[] parent;
        int[] rank;
        int[] Size;
        public UnionFindTree(int size){
            this.parent = new int[size];
            this.rank = new int[size];
            this.Size = new int[size];
            for (int i=0;i<size;i++){
                makeSet(i);
            }
        }
        public void makeSet(int i){
            parent[i]=i;
            rank[i]=0;
            Size[i]=1;
        }
        public void unite(int x, int y){
            int xRoot = find(x);
            int yRoot = find(y);
            if (rank[xRoot]>rank[yRoot]){
                parent[yRoot] = xRoot;
                Size[xRoot]+=Size[yRoot];
            }else if (rank[xRoot]<rank[yRoot]){
                parent[xRoot] = yRoot;
                Size[yRoot]+=Size[xRoot];
            }else if (xRoot!=yRoot){
                parent[yRoot] = xRoot;
                rank[xRoot]++;
                Size[xRoot]+=Size[yRoot];
            }
        }
        public int find(int i){
            if (i!= parent[i]){
                parent[i]=find(parent[i]);
            }
            return parent[i];
        }
        public boolean same(int x, int y){
            return find(x) == find(y);
        }
        public int getSize(int i){return Size[find(i)];}
    }
    public static class BitSearch<T>{
        T[] Array;
        int Width;
        int Length;
        BitSearch(T[] t, int width){
            Array = t;
            Width = width;
            Length = Array.length;
        }
        void start(){
            long max = (long)Math.pow(Width,Length);
            for (long i=0;i<max;i++){
                StringBuilder s = new StringBuilder(Long.toString(i, Width));
                while (s.length()<Length) s.insert(0, "0");
                run(s);
            }
        }
        void run(StringBuilder s){

        }
    }

}
