Problem:
Score : 800 points

Problem Statement

You are given an integer sequence x of length N.
Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.

a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.

For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.

Constraints

1 ≤ N ≤ 500

1 ≤ x_i ≤ N^2

All x_i are distinct.

Input

The input is given from Standard Input in the following format:

N
x_1 x_2 ... x_N

Output

If there does not exist an integer sequence a that satisfies all the conditions, print No.
If there does exist such an sequence a, print Yes in the first line, then print an instance of a in the second line, with spaces inbetween.

Sample Input 1

3
1 5 9

Sample Output 1

Yes
1 1 1 2 2 2 3 3 3

For example, the second occurrence of the integer 2 from the left in a in the output is the fifth element of a from the left.
Similarly, the condition is satisfied for the integers 1 and 3.

Sample Input 2

2
4 1

Sample Output 2

No

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

#include <iostream>
#include <iomanip>
#include <fstream>
#include <string>
#include <array>
#include <vector>
#include <deque>
#include <list>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <stack>
#include <queue>
#include <bitset>
#include <tuple>
#include <cmath>
#include <complex>
#include <algorithm>
#include <utility>
#include <regex>
#include <cstdint>
#include <numeric>
#include <functional>
#include <cassert>

using namespace std;
using ll = long long;
using ull = unsigned long long;

constexpr ll INF = 1'000'000'000'000'000'000;
namespace utils{
#define ALL(x) begin(x), end(x)
#define rALL(x) rbegin(x), rend(x)
    template<class T, class Compare> using p_queue = priority_queue<T, vector<T>, Compare>;
    template<class T> using min_queue = p_queue<T, greater<T>>;
    template<class T> using max_queue = p_queue<T, less<T>>;

    template<class T> bool min_update(T& X, const T& A){ if(X > A) {X = A; return true;} return false; }
    template<class T> bool max_update(T& X, const T& A){ if(X < A) {X = A; return true;} return false; }
    using V_Set = unordered_set<int>;
    using E_Set = unordered_map<int, V_Set>;

    ll operator"" _64(unsigned long long x){ return ll(x); }
    ull operator"" _64u(unsigned long long x){ return ull(x); }

    template<class T>
    vector<T> make_vector(int n, T t){
        return vector<T>(n, t);
    }
    template<class ...Ts>
    auto make_vector(int n, Ts ... ts){
        return vector<decltype(make_vector(ts...))>(n, make_vector(ts...));
    }

    template<class T>
    ostream& operator<<(ostream& os, const vector<T>& v){
        for (auto &&x : v) { os << x << ' '; } cout << endl; return os ;
    }
}
using namespace utils;

class solver{
    istream& is;
    ostream& os;

public:
    solver(istream& I, ostream& O) :is(I), os(O) {}
    void run(){
        ll N;
        is >> N;
        if(!is) return;
        vector<ll> a(N*N, -1);
        vector<ll> X(N);
        for (int i = 0; i < N; ++i) {
            int x;
            is >> x; x--;
            a[x] = i+1;
        } // end i
        map<ll, int> rem;
        for (int i = 0; i < a.size(); ++i) {
            if(a[i] != -1){
                if(a[i] != N) rem.insert({a[i], N - a[i]});
            }
            else{
                if(!rem.empty()){
                    auto&& ps = rem.begin();
                    a[i] = ps->first;
                    ps->second--;
                    if(ps->second == 0){
                        rem.erase(ps);
                    }
                }
            }
        } // end i
        if(!rem.empty()){
            os << "No\n"; return;
        }
        map<ll, int> add;
        for (int i = a.size() - 1; i >= 0; --i) {
            if(a[i] != -1){
                rem[a[i]]++;
                if(rem[a[i]] == N - a[i] + 1){
                    add[a[i]] = a[i] - 1;
                }
            }
            else{
                while(!add.empty() and add.begin()->second == 0) add.erase(add.begin());
                if(add.empty()) {
                    os << "No\n"; return;
                }
                a[i] = add.begin()->first;
                add.begin()->second--;
            }
        } // end i

        os << "Yes\n";
        for (auto &&ai : a) {
            os << ai << ' ' ;
        } // end ai
        os << endl;

    }
};

int main(int argc, char *argv[]) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << setprecision(16) << scientific;
#ifdef DEBUG
    string test_cases = "test_K-thK.txt";
    cerr << test_cases << " -->" << endl;
    auto fs = fstream(test_cases, fstream::in);
    int loop = 0;
    while(fs) {
        loop++;
        cout << '#' << loop << "#------\n";
        solver(fs, cout).run();
    }
    if(loop <= 1) {
        cout << "===" << endl;
        while(cin) solver(cin, cout).run();
    }
#else
    solver(cin, cout).run();
#endif
    return 0;
}