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 <bits/stdc++.h>
using namespace std;

using i64 = int64_t;

#define rep(i, x, y) for (i64 i = i64(x), i##_max_for_repmacro = i64(y); i < i##_max_for_repmacro; ++i)
#define debug(x) #x << "=" << (x)

#ifdef DEBUG
#define _GLIBCXX_DEBUG
#define print(x) std::cerr << debug(x) << " (L:" << __LINE__ << ")" << std::endl
#else
#define print(x)
#endif

const int inf = 1.01e9;
const i64 inf64 = 4.01e18;
const double eps = 1e-9;

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
    os << "[";
    for (const auto &v : vec) {
        os << v << ",";
    }
    os << "]";
    return os;
}

template <typename T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <typename T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

void solve() {
    //const i64 mod = 1'000'000'007;
    i64 N;
    cin >> N;

    vector<i64> b(N);
    rep(i,0,N){
        cin >> b[i];
        --b[i];
    }

    vector<i64> cnt(N);
    rep(i,0,N){
        ++cnt[b[i]];
    }

    rep(i,0,N){
        if(cnt[i]>N-i){
            cout << -1 << endl;
            return;
        }
    }

    vector<i64> v=b,ans;
    rep(i,0,N){
        i64 maxi=-1,pos=-1;
        rep(j,0,v.size()){
            if(j!=v[j]) continue;
            if(maxi<v[j]){
                maxi=v[j];
                pos=j;
            }
        }
        if(maxi>N-1-i or pos==-1){
            cout << -1 << endl;
            return;
        }
        ans.emplace_back(v[pos]);
        v.erase(begin(v)+pos);
    }

    reverse(begin(ans),end(ans));
    rep(i,0,N){
        cout << ans[i]+1 << endl;
    }
}

int main() {
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);
    cout.setf(ios::fixed);
    cout.precision(16);
    solve();
    return 0;
}