#include <bits/stdc++.h>
using namespace std;
const int MAXN = 500000;

// SPF array for precomputing Smallest Prime Factors
vector<int> spf(MAXN + 1);

void computeSPF() {
    iota(spf.begin(), spf.end(), 0); // Initialize spf[i] = i
    for (int i = 2; i * i <= MAXN; ++i) {
        if (spf[i] == i) { // Prime number found
            for (int j = i * i; j <= MAXN; j += i) {
                if (spf[j] == j) spf[j] = i; // Update smallest prime factor
            }
        }
    }
}

void solve() {
    int n;
    cin >> n;
    vector<int> C(n + 1);
    for (int i = 1; i <= n; ++i) cin >> C[i];

    // Group indices by their Smallest Prime Factor
    unordered_map<int, vector<int>> groups;
    for (int i = 1; i <= n; ++i) {
        groups[spf[i]].push_back(i);
    }

    vector<int> A(n + 1, 0);
    
    // Process each SPF group independently
    for (auto &[prime, indices] : groups) {
        vector<pair<int, int>> indexedC;
        for (int idx : indices) {
            indexedC.emplace_back(C[idx], idx);
        }
        
        // Sort by C[i] (we need to construct valid ordering)
        sort(indexedC.begin(), indexedC.end());
        
        int size = indices.size();
        vector<int> sortedValues(size);
        iota(sortedValues.begin(), sortedValues.end(), 1); // Assign values from 1 to size

        for (int i = 0; i < size; ++i) {
            int expected = indexedC[i].first;
            if (expected != i) {
                cout << "NO\n";
                return;
            }
            A[indexedC[i].second] = sortedValues[i] + 1; // Assign increasing values
        }
    }

    cout << "YES\n";
    for (int i = 1; i <= n; ++i) cout << A[i] << " ";
    cout << "\n";
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    computeSPF(); // Precompute SPF values

    int t;
    cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}