Did Bila'am Say Tachanun?

The pasuk relays Balak's disappointment in Bila'am when it states (Bamidbar 23:11)

"לקב איבי לקחתיך והנה ברכת ברך"

"I hired you to curse my enemies and behold you have blessed them."

The Chasam Sofer points out that in an average Jewish year there are 354 days. Of these there are 222 days that we say Tachanun and are considered to be somewhat days of judgment. Conversely, there are 132 days that we do not say Tachanun because they are days of joy. Bila'am was hired to make our entire year into days of judgment and leave us no happiness. The Gematria of לקב (to curse) from the earlier verse is 132 and ברך (bless) is 222. Bila'am blessed us with such a blessing that not only did our days of happiness not turn to judgment, but those of judgment turned to happiness.