Codeforces Round #645 (Div. 2) A. Park Lighting

Due to the coronavirus pandemic, city authorities obligated citizens to keep a social distance. The mayor of the city Semyon wants to light up Gluharniki park so that people could see each other even at night to keep the social distance.

The park is a rectangular table with nn rows and mm columns, where the cells of the table are squares, and the boundaries between the cells are streets. External borders are also streets. Every street has length 11. For example, park with n=m=2n=m=2 has 1212 streets.

You were assigned to develop a plan for lighting the park. You can put lanterns in the middle of the streets. The lamp lights two squares near it (or only one square if it stands on the border of the park).

The park sizes are: n=4n=4, m=5m=5. The lighted squares are marked yellow. Please note that all streets have length 11. Lanterns are placed in the middle of the streets. In the picture not all the squares are lit.

Semyon wants to spend the least possible amount of money on lighting but also wants people throughout the park to keep a social distance. So he asks you to find the minimum number of lanterns that are required to light all the squares.

Input

The first line contains a single integer tt (1≤t≤1041≤t≤104) — the number of test cases in the input. Then tt test cases follow.

Each test case is a line containing two integers nn, mm (1≤n,m≤1041≤n,m≤104) — park sizes.

Output

Print tt answers to the test cases. Each answer must be a single integer — the minimum number of lanterns that are required to light all the squares.

Example

Input

Copy

5
1 1
1 3
2 2
3 3
5 3

Output

Copy

1
2
2
5
8
只会分类讨论的垃圾解法==

#include <bits/stdc++.h>
using namespace std;
int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        int n,m;
        cin>>n>>m;
        if(n%2==0)
        {
            cout<<m*(n/2)<<endl;
        }
        else if(m%2==0)
        {
            cout<<n*(m/2)<<endl;
        }
        else
        {
            cout<<m*(n/2)+m/2+1<<endl;
        }
    }
}