#include <iostream>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <iomanip>
using namespace std;

const int N = 2e5 + 5, inf = 1e9, mod = 1e9 + 9;
#define pb push_back
#define mp make_pair
#define ll long long
#define ff first
#define ss second
#define all(a) a.begin(),a.end()
#define sz(x) (int)x.size()
typedef vector<int> vi;
typedef pair<int,int> ii;
typedef vector<ii> vii;

ll ba[1000006];
ll hort[1000006];

ll binpow(ll a, ll b, ll m){
    a %= m;
    ll res = 1;
    while(b > 0){
        if(b & 1)
            res = res * a % m;
        a = a * a % m;
        b >>= 1;
    }
    return res;
}
ll inverse(ll x){
    return binpow(x, mod - 2, mod);
}

void solve(){
    ll n;
    cin >> n;
    vi a(n);
    ll sum = 0;
    ll ans = 1;
    map<int, int> mp;
    for(ll i = 0; i < n; i++){
        cin >> a[i];
        mp[a[i]]++;
        sum += a[i];
    }
    
    if(n % 2 == 1){
        if(sum % n != 0){
            cout << 0 << '\n';
            return;
        }
        else sum = sum / n * 2;

        if(mp[sum / 2] == 0){
            cout << 0 << '\n';
            return;
        }

        mp[sum / 2]--;
        map<int, int> boo;
        for(int i = 0; i < n; i++){
            ll cnt = 0;
            cnt = mp[a[i]];
            if(boo[a[i]] == 1) continue;
            if(a[i] * 2 == sum){
                if(a[i] % 2 == 1){
                    cout << 0 << '\n';
                    return;
                }
                cnt = 1;
                boo[a[i]] = 1;
            }

            if(mp[sum - a[i]] != mp[a[i]]){
                cout << -1 << '\n';
                return;
            }
            ans *=(1LL * hort[mp[a[i]]]);
            ans %= mod;
            ans *= inverse(ba[cnt]);
            boo[sum - a[i]] = 1;
            boo[a[i]] = 1;
        }
    }

    else{
        ll tmp = n / 2;
        if(sum % tmp != 0){
            cout << 0 << '\n';
            return;
        }
        else sum = sum / tmp;
        map<int, int> boo;
        for(int i = 0; i < n; i++){
            ll cnt = 0;
            if(boo[a[i]] == 1) continue;

            if(mp[sum - a[i]] != mp[a[i]]){
                cout << -1 << '\n';
                return;
            }

            cnt = mp[a[i]];
            ans *=(1LL * hort[mp[a[i]]]);
            ans %= mod;
            ans *= inverse(ba[cnt]);
            boo[sum - a[i]] = 1;
            boo[a[i]] = 1;
        }
    }
    while(ans < 0) ans += mod;
    cout << ans << '\n';
}

int main(){
    // ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    int t = 1;
    ba[1] = 1;
    hort[0] = 1;
    for(int i = 2; i <= 5 * 1e5 + 5; i++){
        ba[i] = ba[i - 1] * i;
        ba[i] %= mod;
    }
    for(int i = 1; i <= 5 * 1e5 + 5; i++){
        hort[i] = hort[i - 1] * 2;
        hort[i] %= mod;
    }
    cin >> t;
    while(t--){
        solve();
    }
    return 0;
}