Three Dimensions

Define a strange distance between two points $a=(x_a,y_a,z_a)$ and $b=(x_b,y_b,z_b)$ in three-dimensional space as follows.

$d(a,b)=\max\{|x_a-x_b|,|y_a-y_b|,|z_a-z_b|\} \oplus x_a \oplus y_a \oplus z_a \oplus x_b \oplus y_b \oplus z_b,$

Here $\max\{S\}$ is the maximum value in $S$, $|x|$ is the absolute value of $x$, and $\oplus$ is the bitwise exclusive-or operator.

Given 6 non-negative integers $mx_a, my_a, mz_a, mx_b, my_b, mz_b$, find the sum of $d(a,b)$ over all integer points with $x_a \in [0, mx_a]$, $y_a \in [0, my_a]$, $z_a \in [0, mz_a]$, $x_b \in [0, mx_b]$, $y_b \in [0, my_b]$, and $z_b \in [0, mz_b]$. Since the sum may be very large, output it modulo $2^{30}$.

The input contains 6 non-negative integers $mx_a, my_a, mz_a, mx_b, my_b, mz_b$, each not larger than $10^9$.

Output the sum modulo $2^{30}$ as a single integer.