#include <bits/stdc++.h>
#ifdef Sabbir
#pragma GCC diagnostic ignored "-Wunused-variable"
#pragma GCC diagnostic ignored "-Wsign-compare"
#endif
using namespace std;
#ifdef Sabbir
#include <E:\CodeBox\TempBox\Debug\debug.h>
#else
#define dbg(x...)
#endif

#include <ext/pb_ds/assoc_container.hpp> 
#include <ext/pb_ds/tree_policy.hpp> 
using namespace __gnu_pbds; 
// Ordered set supporting order statistics.
#define ordered_set tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update>

#define ll long long
#define all(x) (x).begin(), (x).end()
#define in(v) for(auto &b: v) cin >> b;
#define pb push_back

// Sieve globals.
vector<int> primes;
const ll mx = 1e6+1;
vector<bool> isprime(mx, true);

// Sieve to generate primes up to mx.
void sieve(){
    isprime[1] = false;
    for (ll i = 2; i * i <= mx; i++){
        if(isprime[i]){
            for (ll j = i * i; j <= mx; j += i){
                isprime[j] = false;
            }
        }
    }
    for (int i = 2; i < mx; i++){
        if(isprime[i])
            primes.pb(i);
    }
}

void pagol(){
    int n;
    cin >> n;
    vector<int> v(n);
    in(v);
    // We'll create groups indexed by their SPF.
    // Since SPF(i) is either 1 (for i==1) or a prime (for i>=2), we allocate an array sized n+1.
    vector<vector<int>> groups(n + 1);
    
    // Process index 1 separately, as SPF(1) = 1.
    groups[1].pb(1);
    int mot = 0;
    // For every number i from 2 to n, compute its smallest prime factor (SPF)
    // by iterating over our precomputed primes.
    for (int i = 2; i <= n; i++){
        for (auto a : primes){
            if (i % a == 0){
                groups[a].pb(i);
                mot = max(mot, a);
                break;
            }
        }
    }
    
    // This will hold our final answer. (1-indexed)
    vector<int> ans(n + 1, 0);
    
    // Process group for SPF = 1 (i.e. index 1)
    {
        int spf = 1;
        if(!groups[spf].empty()){
            // Process indices in descending order.
            reverse(all(groups[spf]));
            ordered_set os;
            for (auto idx : groups[spf]){
                int required = v[idx - 1]; // required inversion count for index idx.
                if (required > os.size()){
                    cout << "NO" << "\n";
                    return;
                }
                if (required == os.size()){
                    // When inversion count equals os.size(), we want A[idx] to be larger than every later element.
                    // Since we store negatives (so that a smaller negative means a larger A value),
                    // we need to insert a new negative value smaller than *os.begin().
                    if (os.size() > 0)
                        os.insert((*os.begin()) - 1);  // Subtracting 1 gives a smaller (more negative) value.
                    else
                        os.insert(-10000000);  // initial value if os is empty
                    ans[idx] = -(*os.begin());
                } else {
                    ans[idx] = -(*os.find_by_order(required));
                }
            }
        }
    }
    
    // Process groups for each prime factor.
    for (auto a : primes){
        if (a > mot) break;
        if (groups[a].empty()) continue;
        reverse(all(groups[a]));
        ordered_set os;
        for (auto idx : groups[a]){
            int required = v[idx - 1];
            if (required > os.size()){
                cout << "NO" << "\n";
                return;
            }
            if (required == os.size()){
                if (os.size() > 0)
                    os.insert((*os.begin()) - 1);  // Correct: subtract 1 to get a new value smaller than the current minimum.
                else
                    os.insert(-10000000);
                ans[idx] = -(*os.begin());
            } else {
                ans[idx] = -(*os.find_by_order(required));
            }
        }
    }
    
    cout << "YES" << "\n";
    for (int i = 1; i <= n; i++){
        cout << ans[i] << " ";
    }
    cout << "\n";
}

int32_t main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    sieve();
    int t;
    cin >> t;
    while (t--){
        pagol();
    }
    return 0;
}