CF1462F The Treasure of The Segments

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 \leq i \leq 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?

The first line contains a single integer $ t $ ( $ 1 \leq t \leq 2 \cdot 10^5 $ ) — number of test cases. Then $ t $ test cases follow. The first line of each test case contains a single integer $ n $ ( $ 1 \leq n \leq 2 \cdot 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 \leq l \leq r \leq 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 \cdot 10^5 $ .

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.