1462_F. The Treasure of The Segments_36690
Polycarp found n segments on the street. A segment with the index i is described by two integers l_i and r_i — coordinates of the beginning and end of the segment, respectively. Polycarp realized that he didn't need all the segments, so he wanted to delete some of them.

Polycarp believes that a set of k segments is good if there is a segment [l_i, r_i] (1 ≤ i ≤ k) from the set, such that it intersects every segment from the set (the intersection must be a point or segment). For example, a set of 3 segments [[1, 4], [2, 3], [3, 6]] is good, since the segment [2, 3] intersects each segment from the set. Set of 4 segments [[1, 2], [2, 3], [3, 5], [4, 5]] is not good.

Polycarp wonders, what is the minimum number of segments he has to delete so that the remaining segments form a good set?

Input

The first line contains a single integer t (1 ≤ t ≤ 2 ⋅ 10^5) — number of test cases. Then t test cases follow.

The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of segments. This is followed by n lines describing the segments.

Each segment is described by two integers l and r (1 ≤ l ≤ r ≤ 10^9) — coordinates of the beginning and end of the segment, respectively.

It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output a single integer — the minimum number of segments that need to be deleted in order for the set of remaining segments to become good.

Example

Input


4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8


Output


0
1
2
0
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Problem problem = new Problem();
        problem.solve();
    }
}

class Problem {

    Parser parser = new Parser();

    void solve() {
        int t = parser.parseInt();
        for (int i = 0; i < t; i++) {
            solve(i);
        }
    }

    void solve(int testcase) {
        int n = parser.parseInt();

        List<Pair> pairsSortL = new ArrayList<>();
        List<Pair> pairsSortR = new ArrayList<>();

        for (int i = 0; i < n; i++) {
            int l = parser.parseInt();
            int r = parser.parseInt();
            pairsSortL.add(new Pair(l, r, i));
            pairsSortR.add(new Pair(l, r, i));
        }

        int[] counts = new int[n];

        pairsSortL.sort(Comparator.comparingInt(Pair::getL));
        pairsSortR.sort(Comparator.comparingInt(Pair::getR));
        int rIndex = 0;
        for (int i = 0; i < n; i++) {
            while (rIndex < n && pairsSortR.get(rIndex).r < pairsSortL.get(i).l) {
                rIndex += 1;
            }
            rIndex -= 1;
            counts[pairsSortL.get(i).index] += (rIndex + 1);
            if (rIndex < 0) {
                rIndex = 0;
            }
        }

        int lIndex = n - 1;
        for (int i = n - 1; i >= 0; i--) {
            while (lIndex >= 0 && pairsSortR.get(i).r < pairsSortL.get(lIndex).l) {
                lIndex -= 1;
            }
            lIndex += 1;
            counts[pairsSortR.get(i).index] += (n - lIndex);
            if(lIndex > n - 1) {
                lIndex = n - 1;
            }
        }

        int ans = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++) {
            ans = Math.min(ans, counts[i]);
        }

        System.out.println(ans);
    }

    static class Pair {
        int l;
        int r;
        int index;

        public Pair(int l, int r, int index) {
            this.l = l;
            this.r = r;
            this.index = index;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return l == pair.l &&
                    r == pair.r;
        }

        @Override
        public int hashCode() {
            return Objects.hash(l, r);
        }

        public int getL() {
            return l;
        }

        public int getR() {
            return r;
        }
    }
}

class Parser {
    BufferedReader reader;
    StringTokenizer tokenizer;

    Parser() {
        this(System.in);
    }

    Parser(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
    }

    void fill() {
        while (tokenizer == null || !tokenizer.hasMoreElements()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }

    int parseInt() {
        fill();
        return Integer.parseInt(tokenizer.nextToken());
    }

    long parseLong() {
        fill();
        return Long.parseLong(tokenizer.nextToken());
    }

    double parseDouble() {
        fill();
        return Double.parseDouble(tokenizer.nextToken());
    }

    String parseString() {
        fill();
        return tokenizer.nextToken();
    }
}
4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 7
1
1 2
1
1 2
1
1 2
1
1 2
1
1 2
1
1 2
1
1 2
 7
1
1 2
1
1 2
1
1 2
1
1 2
1
1 2
1
1 2
1
1 1
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
2 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
2 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
1 8
4 8
 4
3
1 4
1 3
3 6
4
1 2
2 3
5 5
4 5
5
0 2
2 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 1
3 5
4 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
2 5
5
0 0
1 13
4 1
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
4 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
2 8
4 5
6 7
3 10
5
1 5
2 4
3 5
3 8
4 8
 4
3
1 4
4 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
2 8
4 5
6 7
3 10
5
1 1
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
5 6
4
1 2
2 3
3 5
4 5
5
0 4
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 2
3 5
4 5
5
0 2
3 8
4 5
6 7
2 10
5
1 5
2 4
3 5
3 8
4 8
 7
1
1 2
1
1 2
1
1 2
1
1 2
1
1 2
1
1 2
1
1 3
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3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
1 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
2 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
1 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 7
1
1 2
1
1 2
1
1 2
1
2 2
1
1 2
1
1 2
1
1 3
 7
1
1 2
1
1 2
1
1 2
1
2 2
1
1 3
1
1 2
1
1 3
 7
1
1 2
1
1 2
1
1 2
1
2 2
1
1 3
1
1 1
1
1 3
 7
1
1 2
1
1 2
1
2 2
1
2 2
1
1 3
1
1 1
1
1 3
 7
1
1 2
1
1 2
1
2 2
1
2 2
1
1 3
1
1 1
1
1 5
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3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 4
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 7
1
1 1
1
1 2
1
1 2
1
1 2
1
1 2
1
1 2
1
1 3
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3
1 4
1 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
2 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 0
1 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
1 8
4 8
 7
1
1 2
1
1 2
1
1 2
1
2 3
1
1 3
1
1 2
1
1 3
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 4
3 8
4 5
6 7
9 10
5
1 2
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 0
1 8
4 1
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
1 8
3 8
 7
1
1 2
1
1 2
1
1 2
1
3 3
1
1 3
1
1 2
1
1 3
 4
3
1 4
1 3
3 6
4
1 2
2 3
5 5
4 5
5
0 2
2 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 16
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 0
1 13
4 1
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 4
3 5
1 8
3 8
 4
3
1 4
2 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
3 8
 4
3
1 6
2 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
3 8
 4
3
1 6
2 3
3 6
4
0 2
4 3
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
3 8
 4
3
1 4
2 3
3 6
4
0 2
4 3
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
3 8
 4
3
1 4
2 3
3 6
4
0 2
4 3
3 5
2 5
5
0 2
3 7
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
3 8
 7
1
1 2
1
1 2
1
1 3
1
1 2
1
1 2
1
1 2
1
1 1
 4
3
1 4
2 3
3 6
4
1 2
2 2
3 5
4 5
5
0 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
4 8
 4
3
1 4
4 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
2 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
4 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
1 8
4 5
6 7
11 10
5
1 5
2 4
3 5
2 8
4 8
 7
1
1 2
1
1 2
1
1 2
1
2 2
1
1 2
1
1 4
1
1 3
 4
3
2 4
2 3
3 6
4
1 2
2 3
3 5
2 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
1 8
4 8
 7
1
1 2
1
2 2
1
1 2
1
2 2
1
1 3
1
1 1
1
1 3
 4
3
1 4
1 3
3 6
4
1 2
2 3
3 5
4 10
5
0 2
2 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 0
1 8
4 5
6 7
9 10
5
1 5
4 4
3 5
2 8
4 8
 7
1
1 2
1
2 2
1
1 2
1
2 3
1
1 3
1
1 2
1
1 3
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
3 8
4 5
6 7
9 10
5
1 2
2 4
3 5
3 8
4 8
 4
3
1 4
1 3
3 6
4
2 2
2 3
5 5
4 5
5
0 2
2 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 0
1 8
6 1
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
1 1
3 8
 4
3
1 4
1 3
3 6
4
1 2
2 3
5 5
4 5
5
0 0
2 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 16
 4
3
1 4
1 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 4
3 5
1 8
3 8
 4
3
1 4
2 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 3
3 5
1 8
3 8
 4
3
1 6
2 3
3 6
4
1 2
4 2
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
3 8
 4
3
1 4
2 3
3 6
4
0 2
2 3
3 5
2 5
5
0 2
3 7
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
3 8
 4
3
1 4
2 3
3 6
4
1 2
2 1
3 5
4 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
6 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 2
3 5
4 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
4 8
4 10
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 7
1
1 2
1
1 2
1
1 2
1
2 2
1
1 3
1
1 4
1
1 3
 7
1
1 2
1
2 3
1
1 2
1
2 2
1
1 3
1
1 1
1
1 3
 4
3
1 4
1 3
3 6
4
1 2
2 3
3 5
4 10
5
0 2
2 8
4 5
6 7
9 10
5
1 5
2 1
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 0
1 8
4 5
6 7
9 10
5
1 10
4 4
3 5
2 8
4 8
 7
1
1 2
1
2 2
1
1 2
1
2 3
1
1 3
1
1 4
1
1 3
 4
3
1 4
1 3
3 6
4
2 2
2 3
5 5
4 5
5
0 2
1 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
4 3
3 6
4
1 2
2 3
3 5
4 5
5
0 0
1 8
6 1
6 7
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
1 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
1 1
3 8
 4
3
1 4
1 3
3 6
4
1 2
2 3
5 5
4 5
5
0 0
2 8
4 5
6 7
9 10
5
1 9
2 4
3 5
2 8
4 16
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
2 5
5
0 0
1 13
4 1
6 14
9 10
5
1 5
2 4
3 5
2 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 7
5 5
6 7
9 10
5
1 5
2 4
3 5
1 8
3 8
 4
3
1 4
2 6
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 3
3 5
1 8
3 8
 4
3
1 6
2 3
3 6
4
1 2
4 2
3 5
2 5
5
1 2
3 7
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
3 12
 4
3
1 4
2 3
3 6
4
0 1
2 3
3 5
2 5
5
0 2
3 7
4 5
6 7
9 10
5
1 5
2 6
3 5
1 8
3 8
 4
3
1 4
2 3
3 6
4
1 2
2 1
3 5
4 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
6 9
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 2
3 5
4 5
5
1 2
3 8
4 5
4 7
9 10
5
1 5
2 4
3 5
3 8
4 8
 4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
0 2
4 8
4 10
6 7
9 10
5
1 4
2 4
3 5
2 8
4 8
 7
1
1 2
1
1 2
1
1 2
1
2 3
1
1 3
1
1 4
1
1 3
 4
3
1 4
1 3
3 6
4
2 2
2 3
5 5
4 5
5
0 2
1 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 8
4 11
 4
3
1 4
1 3
3 6
4
1 2
4 3
3 5
2 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
2 1
3 8
 4
3
1 4
1 3
3 6
4
1 2
2 3
5 5
4 5
5
0 0
2 8
4 5
6 7
9 10
5
1 9
2 4
3 5
2 2
4 16
 4
3
1 4
2 3
3 6
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