B. Composite Coloring

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// Problem: B. Composite Coloring
// Contest: Codeforces - Codeforces Round #630 (Div. 2)
// URL: https://codeforces.com/problemset/problem/1332/B
// Memory Limit: 512 MB
// Time Limit: 2000 ms
// 2022-03-02 15:11:35
// 
// Powered by CP Editor (https://cpeditor.org)

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

#define rep(i,l,r) for(int i=(l);i<=(r);i++)
#define per(i,l,r) for(int i=(l);i>=(r);i--)
#define ll long long
#define pii pair<int, int>
#define mset(s,t) memset(s,t,sizeof(t))
#define mcpy(s,t) memcpy(s,t,sizeof(t))
#define fi first
#define se second
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define SZ(x) ((int)(x).size())
#define mp make_pair

const ll mod = 1e9 + 7;

inline ll qmi (ll a, ll b) {
    ll ans = 1;
    while (b) {
        if (b & 1) ans = ans * a%mod;
        a = a * a %mod;
        b >>= 1;
    }
    return ans;
}
inline int read () {
    int x = 0, f = 0;
    char ch = getchar();
    while (!isdigit(ch)) f |= (ch=='-'),ch= getchar();
    while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
    return f?-x:x;
}
template<typename T> void print(T x) {
    if (x < 0) putchar('-'), x = -x;
    if (x >= 10) print(x/10);
    putchar(x % 10 + '0');
}
inline ll sub (ll a, ll b) {
    return ((a - b ) %mod + mod) %mod;
}
inline ll add (ll a, ll b) {
    return (a + b) %mod;
}
inline ll inv (ll a) {
    return qmi(a, mod - 2);
}
const int N = 1e5 + 10;
int n;
int a[N];
int ans[N];
vector<int> primes;
int vis[N];
int gcd (int a, int b) {
    return b?gcd(b, a %b) : a;
}
bool check (int tar) {
    if (tar < 2) return 0;
    for (int i =2; i <= tar / i; i ++)
        if (tar % i == 0) return 0;
    return 1;
}
void solve() {
    
    cin >> n;

    for (int i = 1; i <= n ;i ++)
        cin >> a[i];
    memset(vis, 0, sizeof vis);
    int cnt = 0;
    for (int i = 1; i <= n ;i ++) {
        for (int j = 0; j < primes.size(); j ++)
            if (a[i] % primes[j] == 0) {
                if (vis[primes[j]]) 
                    ans[i] = vis[primes[j]];
                else
                    ans[i] = vis[primes[j]] = ++cnt;
                break;
            }
        
    }
    cout << cnt << endl;
    for (int i = 1; i <= n; i ++) cout << ans[i] << " ";
    puts("");
}
int main () {
    
    for (int i = 2; i <= 31; i ++)
        if (check(i)) primes.pb(i);
    int t;
    t =1;
    cin >> t;
    while (t --) solve();
    return 0;
}