#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 = 5e5 + 5, inf = 1e9;
#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;

const int mod = 1e9 + 9;

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 mul(ll a, ll b){
    a %= mod;
    a *= b;
    a %= mod;
    return a;
}
ll add(ll a, ll b){
    a %= mod;
    a += b;
    a %= mod;
    return a;
}

ll inverse(ll x){
    return binpow(x, mod - 2, mod);
}
ll fac[N];
int n;

ll calc(vector<ll> &a, ll t){
    map<pair<ll, ll>, int> cnt;

    int dif = 0;
    for(int i = 0; i < n; i++){
        ll l = a[i], r = t - a[i];
        int idx = lower_bound(all(a), r) - a.begin();
        if(idx < n && a[idx] == r){
            if(l != r){
                dif++;
            }
            if(n % 2 == 0){
                cnt[{min(l, r), max(l, r)}]++;
            } else if(l != r){
                cnt[{min(l, r), max(l, r)}]++;
            }
            
        } else {
            return 0;
        }
    }
    ll ans = mul(mul(fac[n / 2], inverse(n / 2 - sz(cnt) + 1)), binpow(2, dif / 2, mod));
    return ans;
}
void solve(){
    
    cin >> n;
    vector<ll> a(n);

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

    }
    
    //tot / (n + 1) / 2
    ll t = tot / ((n + 1) / 2);
    
    fac[0] = 1;
    for(int i = 1; i <= n; i++){
        fac[i] = mul(fac[i - 1], i);
    }

    sort(all(a));
    ll ans = 0;
    if(n % 2 == 0){
        cout << calc(a, t) << '\n';
    } else {
        for(int i = 0; i < n; i++){
            tot += a[i]; int x = (n + 1) / 2;
            if(tot % x == 0){
                ans = add(ans, calc(a, tot / x));
            }
            tot -= a[i];
        }
        cout << ans << '\n';
    }
    
}

int main(){
    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    int t = 1;
    cin >> t;
    while(t--){
        solve();
    }
    return 0;
}