#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
using minheap = priority_queue<long long, vector<long long>, greater<long long>>;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds; // find_by_order, order_of_key

#define ll long long
#define ld long double
#define MOD 1000000007
#define pie 2*(acos(0.0))
#define yes cout<<"YES\n"
#define no cout<<"NO\n"
#define pb push_back
#define endl '\n'
#define lcm(a,b) (a*b)/(__gcd<ll>(a,b))
#define logb(base,val) log2l(val) / log2l(base)
#define print(v) for(auto e:v) cout<<e<<" "; cout<<endl;
#define printp(v) for(auto e:v) cout<<e.first<<" "<<e.second<<endl;
#define srt(v) sort(v.begin(),v.end())
#define rsrt(v) sort(v.rbegin(),v.rend())
#define life_is_a_race ios::sync_with_stdio(false); cin.tie(nullptr);

bool hoynai(int x,int ind,vector<int>&ans,pbds &s)
{
    if(s.size() <= x) return true;
    auto it = s.find_by_order(x);
    ans[ind] = *it;
    s.erase(it);
    return false;
}
void solve()
{
    int n; cin >> n;
    int a[n+1];
    for(int i=1;i<=n;i++) cin >> a[i];
    if(a[1]) {cout<<"NO"; return;}

    vector<int> ans(n+1);
    ans[1] = 1;

    for(int i=2;i<=n;i++)
    {
        if(ans[i]) continue;
        int cnt = 0;
        for(int j=i;j<=n;j+=i)
        {
            if(ans[j]==0) ++cnt;
        }
        pbds s;
        for(int j=1;j<=cnt;j++) s.insert(j);
        for(int j=i;j<=n;j+=i)
        {
            if(ans[j]) continue;
            if(hoynai(a[j],j,ans,s))
            {
                cout<<"NO\n";
                return;
            }
        }
    }
    cout<<"YES\n";
    for(int i=1;i<=n;i++) cout<<ans[i]<<' '; cout<<'\n';
}
int main()
{
    life_is_a_race
    int t=1; 
    cin>>t;
    for(int i=1;i<=t;i++) solve();
}