Tommy bought a house that costs $$551,000$ by taking out a mortgage with $93\%$ loan$-$to$-$value $($LTV$)$ from Ciri bank.

Ciri bank required Tommy to purchase private mortgage insurance $($PMI$)$ for the proportion of the loan over $70\%$ LTV$.$ Ciri bank then insured the rest of the loan with a GSE.

Ten years later, Tommy defaulted. The remaining balance of the mortgage at default was $$365,000$ and the property was sold for $$125,000$ in foreclosure auction.

The insuring GSE lost $ $\_\_\_$ because of this default.