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 atexit, io, sys 
buffer = io.BytesIO() 
sys.stdout = buffer
@atexit.register 
def write(): sys.__stdout__.write(buffer.getvalue())   
##################################### 

import collections

def bs(ais, s):
	lo, hi = 0, len(ais) - 1
	while(lo <hi):
		med = (lo + hi)//2
		if ais[med][0] > s:
			hi = med
		else:
			lo = med +1
	if ais[lo][0] > s:
		return len(ais) - lo
	return 0

def bss(ais, s):
	lo, hi = 0, len(ais) - 1
	while(lo < hi):
		med = (lo + hi + 1)//2
		if ais[med][1] < s:
			lo = med
		else:
			hi = med -1
	return (lo +1) if ais[lo][1] < s else 0

def f(ais):
	ais.sort(key = lambda x:x[0])
	bis = [a for a in ais]
	ais.sort(key = lambda x:x[1])
	cis = [a for a in ais]
	ans = len(ais)
	for u,v in ais:
		ans = min(ans, bs(bis,v) + bss(cis, u))
	return ans
for u in range(int(raw_input())): 
	n = int(raw_input())
	ais = [map(int, raw_input().split()) for _ in range(n)]
	print f(ais)