Problem $3.[35$ points$]$ Write a C$++$ program to

$(1)$ Generate a $2$D pattern with $101$ rows and $101$ columns using a nested

loop as follows: At the location $(i,j),$ that is the $i^{th}$ row and $j^{th}$ column,

print out $\text{'}x\text{'}$ if the distance between this location and the center of the grid

$(51,51)$ is less than $30\mathrm{.}0.$ Otherwise, print out $\text{'}\text{'}.$

$(2)$ The routine automatically saves the pattern to a text file "pattern.txt$".$