What is the piece of music called to which "The animals went in two by two, hurrah!" is sung?

The one I know is exclusively about ants (with thumbs and shoes):

https://www.youtube.com/watch?v=xozQnsGkHJ4

"When Johnny Comes Marching Home" (sometimes "When Johnny Comes Marching Home Again") is a song of the American Civil War that expressed people's longing for the return of their friends and relatives who were fighting in the war.
The tune is that of the Irish antiwar song "Johnny I Hardly Knew Ye", generally presumed to be the original, although no published version is known to pre-date "When Johnny Comes Marching Home Again" [1]. The same tune is used for the children's songs "The Ants Go Marching One By One" and also "The Animals Went in Two by Two". The lyrics, written by Irish-American bandleader Patrick Gilmore, effectively reverse those of the original, in which Johnny returns home blind and crippled, to the woman he abandoned in order to join the army. The larcenous tendencies of the Union soldiers in New Orleans were parodied in the Confederate lyrics, "For Bales", to the same tune.

https://en.wikipedia.org/wiki/When_Johnny_Comes_Marching_Home

This would be my guess, Rise And Shine (also known as Arky Arky)
The Lord said to Noah, "There's gonna be a flood-y, flood-y!"
The Lord said to Noah, "There's gonna be a flood-y, flood-y!
Get those animals out of the mud-dy, mud-dy!" Children of the Lord.
(chorus: So rise and shine and give God your glory, glory.
Rise and shine and give God your glory, glory.
Rise and shine and give God your glory, glory. Children of the Lord.)
Noah he built him, he built him an ark-y, ark-y.
Noah he built him, he built him an ark-y, ark-y.
Made it out of wood and bark-y, bark-y. Children of the Lord.
(chorus)
The animals, they came on. They came on by twoosies, twoosies.
The animals, they came on. They came on by twoosies, twoosies.
Elephants and kangaroosies, roosies. Children of the Lord.
(chorus)
It rained and poured for forty daysies, daysies.
It rained and poured for forty daysies, daysies.
Must have driven those animals crazy, crazy. Children of the Lord.
(chorus)
The sun came out and dried up all the landy, landy.
The sun came out and dried up all the landy, landy.
Everything was fine and dandy dandy. Children of the Lord.
(chorus)
The animals, they came off. They came off by threesies, threesies.
The animals, they came off. They came off by threesies, threesies.
Must have been those birds and beezies, beezies. Children of the Lord.
(chorus)
This is the end of, the end of the story, story.
This is the end of, the end of the story, story.
Everything is hunky dory, dory. Children of the Lord.
(chorus)

We used to sing that at summer camp, dp, so you've brought back some pleasurable memories. However, the tune was quite different from the "ants" and "animals" song, which, as Brainy's site says, did employ the melody of "When Johnny Comes Marching Home."

Thanks folks