An integer has a baby if its square root appears inside it.
To be inside, there must be at least one parental digit on either side of the baby.
A baby is happy if it is perfectly centered within its parent integer, ie the same number of digits to its left and to its right.
A baby is healthy if the baby does not contain any zeros.

For example, the square root of 62500 is 250, so 62500 has a happy, but unhealthy baby.
The square root of 214651801 is 14651, so 214651801 has a healthy but unhappy baby. This baby has one digit to its left, but three digits to its right.

Find the first 4 integers with happy, healthy babies.