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

#define FAST ios_base::sync_with_stdio(false);cin.tie(NULL);
using ll = long long;

const int MX = 10000005;
int spf[MX], primes[MX], PIND;
map<int,vector<int>> G;
void gen_spf(int n) {
  int i, j;
  for (i = 1; i <= n; i += 1) spf[i] = i;
  for (i = 2; i <= n; i += 2) spf[i] = 2;
  for (i = 3; i <= n; i += 2) {
    if (spf[i] != i) continue;
    for (j = i; j <= n; j += i) {
      spf[j] = min(spf[j], i);
    }
  }
  for (i = 1; i <= n; ++i) G[spf[i]].push_back(i);
  PIND = 0;
  for (i = 2; i <= n; ++i) {
    if (i == spf[i]) primes[PIND++] = i;
  }
  primes[PIND++] = 1;
}

int main() {
  FAST;
  gen_spf(MX-1);
  
  int tc = 1, ti;
  cin >> tc;

  for (ti = 1; ti <= tc; ++ti) {
    int n, i, j, p, pi;
    cin >> n;

    vector<int> a(n);
    for (i = 0; i < n; ++i) cin >> a[i];

    vector<set<int>> at(n+1);
    for (i = 0; i < n; ++i) at[a[i]].emplace(i);
    
    bool f = 1;
    vector<vector<int>> inds;
    vector<int> ans(n, 0);
    j = n;
    while (j >= 0) {
      while (!at[j].empty()) {
        vector<int> curr;
        auto it = at[j].begin();
        curr.push_back(*it);
        at[j].erase(it);
        for (i = j-1; i >= 0; --i) {
          auto it = at[i].lower_bound(curr.back());
          if (it == at[i].end()) {
            f = 0;
            break;
          }
          curr.push_back(*it);
          at[i].erase(it);
        }
        if (!f) break;
        inds.push_back(curr);
      }
      if (!f) break;
      --j;
    }

    if (f) {
      sort(inds.begin(), inds.end(), [&](auto& x, auto& y) {
        return ((int)x.size() < (int)y.size());
      });
  
      pi = 0;
      while (!inds.empty()) {
        auto& curr_inds = inds.back();
        assert(pi < PIND);
        p = primes[pi];
        j = (int)G[p].size();
        for (int x : curr_inds) {
          --j;
          assert(j >= 0);
          ans[x] = G[p][j];
        }
        inds.pop_back();
        ++pi;
      }
    }

    if (f) {
      cout << "YES" << "\n";
      for (i = 0; i < n; ++i) cout << ans[i] << " ";
      cout << "\n";
    } else {
      cout << "NO" << "\n";
    }
  }

  return 0;
}