On August $31,2022,$ Nolan and Lei, who file a joint return and live in Charleston, South Carolina, sell their personal residence, which they have owned and lived in for $10$ years. The realized gain of $$292,000$ was excluded under $$121.$ They purchased another personal residence in Charleston for $$480,000$ on September $1,2022.$

In $2023,$ Nolan's employer transfers him to Houston, Texas. The couple sells the Charleston home on February $28,2023,$ and purchases a new home in Houston. The realized gain on the second sale is $$180,000.$

Do not round any division.

What is Nolan and Lei's recognized gain on the second sale?