13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5fb,

Mr. Chanek just won the national chess tournament and got a huge chessboard of size $$$N \times M$$$. Bored with playing conventional chess, Mr. Chanek now defines a function $$$F(X, Y)$$$, which denotes the minimum number of moves to move a knight from square $$$(1, 1)$$$ to square $$$(X, Y)$$$. It turns out finding $$$F(X, Y)$$$ is too simple, so Mr. Chanek defines:

$$$G(X, Y) = \sum_{i=X}^{N} \sum_{j=Y}^{M} F(i, j)$$$

Given X and Y, you are tasked to find $$$G(X, Y)$$$.

A knight can move from square $$$(a, b)$$$ to square $$$(a', b')$$$ if and only if $$$|a - a'| \gt 0$$$, $$$|b - b'| \gt 0$$$, and $$$|a - a'| + |b - b'| = 3$$$. Of course, the knight cannot leave the chessboard.

Input

The first line contains an integer $$$T$$$ $$$(1 \le T \le 100)$$$, the number of test cases.

Each test case contains a line with four integers $$$X$$$ $$$Y$$$ $$$N$$$ $$$M$$$ $$$(3 \leq X \leq N \leq 10^9, 3 \leq Y \leq M \leq 10^9)$$$.

Captain of Knights

Examples