Polycarp plays a well-known computer game (we won't mention its name). In this game, he can craft tools of two types — shovels and swords. To craft a shovel, Polycarp spends two sticks and one diamond; to craft a sword, Polycarp spends two diamonds and one stick.

Each tool can be sold for exactly one emerald. How many emeralds can Polycarp earn, if he has a sticks and b diamonds?

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

The only line of each test case contains two integers a and b (0 ≤ a, b ≤ 10^9) — the number of sticks and the number of diamonds, respectively.

Output

For each test case print one integer — the maximum number of emeralds Polycarp can earn.

Example

Input


4
4 4
1000000000 0
7 15
8 7


Output


2
0
7
5

Note

In the first test case Polycarp can earn two emeralds as follows: craft one sword and one shovel.

In the second test case Polycarp does not have any diamonds, so he cannot craft anything.
import bisect, math

def foo(a, b):
	return min(a,b,(a+b)//3)

t = int(input())
for _ in range(t):
	# n = int(input())
	# arr.sort()
	# n = int(input())
	# for _ in range(n):
	#     q=int(input())
	#     print(bisect.bisect(arr, q))
	a, b = map(int, input().split())
	print(foo(a, b))
	# arr = list(map(int, input().split()))
	# # a, b = map(int, input().split())
	# for row in foo(n):
		# print(" ".join(map(str, row)))
	# print(" ".join(map(str, foo(n, m))))