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 sys

t = int(input())
for i in range(t):
    inp = input().split()
    a = int(inp[0])
    b = int(inp[1])
    count = 0
    if a==0 or b==0:
        a = -1
        b = -1
    if a==1 and b==1:
        a = -1
        b = -1
    if b>a and a>0:
        if b>=2*a:
            count += a
            a = 0
            b = 0
        else:
            count += a - b
            b = 2*b - a
            a = b
    if a>b and b>0:
        if a>=2*b: 
            count += b
            a = 0
            b = 0
        else:
            count += a - b
            b = 2*b - a
            a = b
    if a>1:
        count += int(2*a/3)
        print(count)
    else: print(count)
