You are given an undirected graph consisting of n vertices and n edges. It is guaranteed that the given graph is connected (i. e. it is possible to reach any vertex from any other vertex) and there are no self-loops and multiple edges in the graph.

Your task is to calculate the number of simple paths of length at least 1 in the given graph. Note that paths that differ only by their direction are considered the same (i. e. you have to calculate the number of undirected paths). For example, paths [1, 2, 3] and [3, 2, 1] are considered the same.

You have to answer t independent test cases.

Recall that a path in the graph is a sequence of vertices v_1, v_2, …, v_k such that each pair of adjacent (consecutive) vertices in this sequence is connected by an edge. The length of the path is the number of edges in it. A simple path is such a path that all vertices in it are distinct.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices (and the number of edges) in the graph.

The next n lines of the test case describe edges: edge i is given as a pair of vertices u_i, v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i), where u_i and v_i are vertices the i-th edge connects. For each pair of vertices (u, v), there is at most one edge between u and v. There are no edges from the vertex to itself. So, there are no self-loops and multiple edges in the graph. The graph is undirected, i. e. all its edges are bidirectional. The graph is connected, i. e. it is possible to reach any vertex from any other vertex by moving along the edges of the graph.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print one integer: the number of simple paths of length at least 1 in the given graph. Note that paths that differ only by their direction are considered the same (i. e. you have to calculate the number of undirected paths).

Example

Input


3
3
1 2
2 3
1 3
4
1 2
2 3
3 4
4 2
5
1 2
2 3
1 3
2 5
4 3


Output


6
11
18

Note

Consider the second test case of the example. It looks like that:

<image>

There are 11 different simple paths:

  1. [1, 2]; 
  2. [2, 3]; 
  3. [3, 4]; 
  4. [2, 4]; 
  5. [1, 2, 4]; 
  6. [1, 2, 3]; 
  7. [2, 3, 4]; 
  8. [2, 4, 3]; 
  9. [3, 2, 4]; 
  10. [1, 2, 3, 4]; 
  11. [1, 2, 4, 3]. 
import java.util.*;
import java.io.*;
import java.awt.*;
import java.math.*;

public class Main implements Runnable {
    @Override
    public void run() {
        try {
            new Solver().solve();
            System.exit(0);
        } catch (Exception | Error e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    public static void main(String[] args) throws Exception {
        //new Thread(null, new Main(), "Solver", 1l << 25).start();
        new Main().run();
    }
}


class Solver {
    final Helper hp;
    final int MAXN = 1000_006;
    final long MOD = (long) 1e9 + 7;

    final Timer timer;
    final TimerTask task;
    final static boolean DEBUG = false; //System.getenv("DEBUG") != null;

    Solver() {
        hp = new Helper(MOD, MAXN);
        if (DEBUG) {
            hp.initIO(System.getProperty("user.home") + "/Desktop/input.txt",
                    System.getProperty("user.home") + "/Desktop/output.txt");
        } else {
            hp.initIO(System.in, System.out);
        }

        timer = new Timer();
        task = new TimerTask() {
            @Override
            public void run() {
                try {
                    hp.flush();
                    System.exit(0);
                } catch (Exception e) {
                }
            }
        };
        //timer.schedule(task, 4700);
    }

    void solve() throws Exception {
        int tc = TESTCASES ? hp.nextInt() : 1;
        for (int tce = 1; tce <= tc; ++tce) solve(tce);
        timer.cancel();
        hp.flush();
    }

    static final boolean TESTCASES = true;

    void solve(int tc) throws Exception {
        int i, j, k;

        N = hp.nextInt();
        graph = new ArrayList[N];
        for (i = 0; i < N; ++i) graph[i] = new ArrayList<>();
        for (i = 0; i < N; ++i) {
            int a = hp.nextInt() - 1, b = hp.nextInt() - 1;
            graph[a].add(b); graph[b].add(a);
        }

        idx = new int[N];
        count = new int[N + 1];
        findCycle(0, -7, new ArrayDeque<>(), new boolean[N]);
        for (i = 0; i < N; ++i) if (idx[i] > 0) {
            for (int itr : graph[i]) if (idx[itr] == 0) {
                assignNumber(itr, idx[i]);
            }
        }

        long ans = 0;
        for (i = 0; i < N; ++i) {
            ans += count[idx[i]] - 1;
            ans += 2 * (N - count[idx[i]]);
        }
        hp.println(ans >> 1);
    }

    int N;
    ArrayList<Integer>[] graph;
    int[] idx, count;

    boolean findCycle(int node, int parent, ArrayDeque<Integer> path, boolean[] vis) {
        if (vis[node]) {
            int num;
            for (num = 1; path.peekLast() != node; ++num) {
                idx[path.pollLast()] = num;
                ++count[num];
            }
            idx[node] = num;
            ++count[num];
            return true;
        }
        vis[node] = true;
        path.addLast(node);

        for (int itr : graph[node]) if (itr != parent) {
            if (findCycle(itr, node, path, vis)) return true;
        }

        path.pollLast();
        vis[node] = false;
        return false;
    }

    void assignNumber(int node, int num) {
        if (idx[node] > 0) return;
        idx[node] = num; ++count[num];
        for (int itr : graph[node]) assignNumber(itr, num);
    }
}

class Helper {
    final long MOD;
    final int MAXN;
    final Random rnd;

    public Helper(long mod, int maxn) {
        MOD = mod;
        MAXN = maxn;
        rnd = new Random();
    }

    public static int[] sieve;
    public static ArrayList<Integer> primes;

    public void setSieve() {
        if (sieve == null || sieve.length < MAXN) {
            primes = new ArrayList<>();
            sieve = new int[MAXN];
            int i, j;
            for (i = 2; i < MAXN; ++i)
                if (sieve[i] == 0) {
                    primes.add(i);
                    for (j = i; j < MAXN; j += i) {
                        sieve[j] = i;
                    }
                }
        }
    }

    public boolean isPrime(int number) {
        setSieve();
        return number <= 1 ? false : sieve[number] == number;
    }

    // https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
    public boolean isProbablePrime(int number, int certainty) {
        if (number < MAXN) return isPrime(number);
        else if ((number & 1) == 0) return false;

        long d = number - 1;
        int r = 0;
        while ((d & 1) == 0) {
            ++r;
            d >>= 1;
        }
        while (--certainty >= 0) { // witness loop
            long a = getRandomInRange(2, Math.min(Integer.MAX_VALUE - 7, number - 2));
            long x = pow(a, d, number);

            if (x == 1 || x == number - 1) {
                continue;
            } else {
                boolean witnessFound = false;
                for (int i = 1; i < r && x > 1; ++i) { // loop runs r - 1 times atmost
                    x = x * x % number;
                    if (x == number - 1) {
                        witnessFound = true;
                        break;
                    }
                }
                if (!witnessFound) return false;
            }
        }
        return true;
    }

    public static long[] factorial;

    public void setFactorial() {
        factorial = new long[MAXN];
        factorial[0] = 1;
        for (int i = 1; i < MAXN; ++i) factorial[i] = factorial[i - 1] * i % MOD;
    }

    public long getFactorial(int n) {
        if (factorial == null) setFactorial();
        return factorial[n];
    }

    public long ncr(int n, int r) {
        if (r > n) return 0;
        if (factorial == null) setFactorial();
        long numerator = factorial[n];
        long denominator = factorial[r] * factorial[n - r] % MOD;
        return numerator * pow(denominator, MOD - 2, MOD) % MOD;
    }


    public long[] getLongArray(int size) throws Exception {
        long[] ar = new long[size];
        for (int i = 0; i < size; ++i) ar[i] = nextLong();
        return ar;
    }

    public int[] getIntArray(int size) throws Exception {
        int[] ar = new int[size];
        for (int i = 0; i < size; ++i) ar[i] = nextInt();
        return ar;
    }

    public String[] getStringArray(int size) throws Exception {
        String[] ar = new String[size];
        for (int i = 0; i < size; ++i) ar[i] = next();
        return ar;
    }

    public String joinElements(long... ar) {
        StringBuilder sb = new StringBuilder();
        for (long itr : ar) sb.append(itr).append(" ");
        return sb.toString().trim();
    }

    public String joinElements(int... ar) {
        StringBuilder sb = new StringBuilder();
        for (int itr : ar) sb.append(itr).append(" ");
        return sb.toString().trim();
    }

    public String joinElements(String... ar) {
        StringBuilder sb = new StringBuilder();
        for (String itr : ar) sb.append(itr).append(" ");
        return sb.toString().trim();
    }

    public String joinElements(Object... ar) {
        StringBuilder sb = new StringBuilder();
        for (Object itr : ar) sb.append(itr).append(" ");
        return sb.toString().trim();
    }

    public long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    public int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    public long max(long... ar) {
        long ret = ar[0];
        for (long itr : ar) ret = Math.max(ret, itr);
        return ret;
    }

    public int max(int... ar) {
        int ret = ar[0];
        for (int itr : ar) ret = Math.max(ret, itr);
        return ret;
    }

    public long min(long... ar) {
        long ret = ar[0];
        for (long itr : ar) ret = Math.min(ret, itr);
        return ret;
    }

    public int min(int... ar) {
        int ret = ar[0];
        for (int itr : ar) ret = Math.min(ret, itr);
        return ret;
    }

    public long sum(long... ar) {
        long sum = 0;
        for (long itr : ar) sum += itr;
        return sum;
    }

    public long sum(int... ar) {
        long sum = 0;
        for (int itr : ar) sum += itr;
        return sum;
    }

    public void shuffle(int[] ar) {
        int r;
        for (int i = 0; i < ar.length; ++i) {
            r = rnd.nextInt(ar.length);
            if (r != i) {
                ar[i] ^= ar[r];
                ar[r] ^= ar[i];
                ar[i] ^= ar[r];
            }
        }
    }

    public void shuffle(long[] ar) {
        int r;
        for (int i = 0; i < ar.length; ++i) {
            r = rnd.nextInt(ar.length);
            if (r != i) {
                ar[i] ^= ar[r];
                ar[r] ^= ar[i];
                ar[i] ^= ar[r];
            }
        }
    }

    public void reverse(int[] ar) {
        int r;
        for (int i = 0; i < ar.length; ++i) {
            r = ar.length - 1 - i;
            if (r > i) {
                ar[i] ^= ar[r];
                ar[r] ^= ar[i];
                ar[i] ^= ar[r];
            }
        }
    }

    public void reverse(long[] ar) {
        int r;
        for (int i = 0; i < ar.length; ++i) {
            r = ar.length - 1 - i;
            if (r > i) {
                ar[i] ^= ar[r];
                ar[r] ^= ar[i];
                ar[i] ^= ar[r];
            }
        }
    }

    public long pow(long base, long exp, long MOD) {
        base %= MOD;
        long ret = 1;
        while (exp > 0) {
            if ((exp & 1) == 1) ret = ret * base % MOD;
            base = base * base % MOD;
            exp >>= 1;
        }
        return ret;
    }

    public int getRandomInRange(int l, int r) {
        return rnd.nextInt(r - l + 1) + l;
    }


    static final int BUFSIZE = 1 << 20;
    static byte[] buf;
    static int index, total;
    static InputStream in;
    static BufferedWriter bw;

    public void initIO(InputStream is, OutputStream os) {
        try {
            in = is;
            bw = new BufferedWriter(new OutputStreamWriter(os));
            buf = new byte[BUFSIZE];
        } catch (Exception e) {
        }
    }

    public void initIO(String inputFile, String outputFile) {
        try {
            in = new FileInputStream(inputFile);
            bw = new BufferedWriter(new OutputStreamWriter(
                    new FileOutputStream(outputFile)));
            buf = new byte[BUFSIZE];
        } catch (Exception e) {
        }
    }

    private int scan() throws Exception {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0)
                return -1;
        }
        return buf[index++];
    }

    public String next() throws Exception {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan())
            sb.append((char) c);
        return sb.toString();
    }

    public int nextInt() throws Exception {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }

    public long nextLong() throws Exception {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }

    public void print(Object a) throws Exception {
        bw.write(a.toString());
    }

    public void printsp(Object a) throws Exception {
        print(a);
        print(" ");
    }

    public void println() throws Exception {
        bw.write("\n");
    }

    public void println(Object a) throws Exception {
        print(a);
        println();
    }

    public void errprint(Object a) {
        if (Solver.DEBUG) {
            System.err.print(a);
        }
    }

    public void errprintsp(Object a) {
        errprint(a);
        errprint(" ");
    }

    public void errprintln() {
        errprint("\n");
    }

    public void errprintln(Object a) {
        errprint(a);
        errprintln();
    }

    public void flush() throws Exception {
        bw.flush();
    }
}
