Does Flesh to Stone count the first saving throw?

Flesh to Stone states:

You attempt to turn one creature that you can see within range into stone. If the target’s body is made of flesh, the creature must make a Constitution saving throw. On a failed save, it is restrained as its flesh begins to harden. On a successful save, the creature isn’t affected.

A creature restrained by this spell must make another Constitution saving throw at the end of each of its turns. If it successfully saves against this spell three times, the spell ends. If it fails its saves three times, it is turned to stone and subjected to the petrified condition for the duration.

My reading of this is that the initial save against the spell counts as one of the failed saves so if the target failed an additional two saves it would be petrified. Is this correct or is the correct interpretation that the target must fail three of the subsequent saves to be petrified?