Yup,the mushroom is a fungi because  typically of the order  the conspicuous umbrella-shaped fruiting body (sporophore) of the fungi, typically of the order Agaricales in the phylum Basidiomycota but also of some other groups. 
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Yes, mushroom is a fungi it belongs to the Class Basidiomycota also known as the club fungi due to its shape.

But, Lato and Guso are both green algaes. They do not belong to the kingdom fungi. They belong to the Kingdom protista class algae. They are seaweeds. but they are different from plants.
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