Given an array a of length n, find another array, b, of length n such that:

  * for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i. 



The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.

If such array doesn't exist, determine this.

Input

The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.

Output

If there's no such array, print a single line containing -1.

Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)

If there are multiple answers, print any.

Examples

Input


3
1 2 3


Output


0 1 2 

Input


4
0 0 0 2


Output


1 3 4 0 

Input


3
1 1 3


Output


0 2 1 

Note

In the second test case, other answers like [1,1,1,0], for example, are valid.
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#pragma comment(linker, "/stack:200000000")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// pragma to turn on excess precision
//#pragma GCC target("fpmath=387")

using namespace std;
using namespace __gnu_pbds;

typedef long long ll;
typedef string str;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector <pii> vpii;
typedef vector <pll> vpll;
typedef map <str,int> mapsi;
typedef map <str,int> :: iterator mapsitr;
typedef map <int , int> mint;
typedef map <ll , ll> mll;
typedef set <int> si;
typedef set <ll> sll;
typedef si :: iterator sitr;
typedef si :: reverse_iterator rsitr;
typedef sll :: iterator sltr;
typedef sll :: reverse_iterator rsltr;
#define mset multiset

typedef mset <int> msi;
typedef mset <ll> msll;
typedef msi :: iterator msitr;
typedef msi :: reverse_iterator msritr;
typedef msll :: iterator msltr;
typedef msll :: reverse_iterator mslritr;

#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
#define ordered_multiset tree<int, null_type,less_equal<int>, rb_tree_tag,tree_order_statistics_node_update>
#define mp make_pair
#define pb push_back
#define pob pop_back
#define pf push_front
#define pof pop_front
#define fi first
#define se second
#define fs first.second
#define ss second.second
#define ff first.first
#define sf second.first
#define newl '\n'
#define fbo find_by_order
#define ook order_of_key
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(),x.rend()
#define watch(x) cout << (#x) << " is : " << (x) << newl

char to_upper (char x){
    if( 97 <= int(x) && int(x) <= 122) return char(x-32);
    if( 65 <= int(x) && int(x) <= 90) return x;
    return -1;
}
char to_lower (char x){
    if( 97 <= int(x) && int(x) <= 122) return x;
    if( 65 <= int(x) && int(x) <= 90) return char(x+32);
    return -1;
}
int numerize (char x){
    if(48 <= int(x) && int(x) <= 57) return int(x-'0');
    if(97 <= int(x) && int(x) <= 122) return int(x-96);
    if(65 <= int(x) && int(x) <= 90) return int(x-64);
    return -1;
}
bool isect (int l1, int r1, int l2, int r2){
    pii p1 = {l1,r1};
    pii p2 = {l2,r2};
    if(p1>p2)swap(p1,p2);
    return (p2.fi <= p1.se);
}
ll quickpow (ll num1, ll num2, ll MOD){
    if(num2==0)return 1%MOD;
    else if(num2==1)return num1%MOD;
    else{
        ll temp = quickpow (num1,num2/2,MOD); ll res = ((temp%MOD) * (temp%MOD))%MOD;
        if(num2%2==1) res = ((res%MOD)*(num1%MOD))%MOD; return res;
    }
}
ll invmod (ll num, ll MOD){return quickpow (num,MOD-2,MOD);}
ll gcd (ll num1, ll num2){
    if(num1 < num2) swap(num1,num2); ll num3 = num1 % num2 ;
    while(num3 > 0){ num1 = num2; num2 = num3; num3 = num1 % num2;}
    return num2;
}
ll lcm (ll num1 , ll num2){return (ll) (num1/__gcd(num1,num2))*num2;}
// end of Template
int n,a[100010],b[100010];
int INF = 1000000;
int main(){

//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);

    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

    cin>>n;
    for(int i=1;i<=n;++i) cin>>a[i];
    int l = 1e6;
    a[n+1] = a[n]+1;
    a[0] = 0;
    for(int i=1;i<=n+1;++i){
        if(a[i] != a[i-1]){
            b[i] = a[i-1];
            int val = a[i-1]+1;
            for(int j=l;j<i;++j){
                if(val >= a[i]){b[j] = INF;}
                else{b[j] = val, ++val;}
            }
            if(val != a[i]) {cout<<-1<<newl; return 0;}
            l = 1e6;
        }
        else{
            l = min(l,i);
        }
    }

    for(int i=1;i<=n;++i) cout<<b[i]<<" ";cout<<newl;


    return 0;
}
