[Request] How high do you throw a water balloon on Mars to freeze it?

Yesterday I was randomly snging too my Alexa the song lyric "Let me see what spring is like on Jupiter and Mars and I learned

"On Mars standing at the equator at high noon

At your feet (surface): The temperature could reach a comfortable 20 degrees Celsius (70 degrees Fahrenheit). This is because the ground absorbs sunlight, warming the air directly above it. At your head (a few feet above the surface): The temperature would be considerably colder, potentially dropping to 0 degrees Celsius (32 degrees Fahrenheit) or even lower. This drastic difference is due to the thin Martian atmosphere's inability to retain heat effectively. The warmth from the ground radiates away quickly, leading to much colder temperatures at slightly higher altitudes. "

This led to the question assuming I toss a water balloon from the ground and then catch it again at the ground, how high do I have to throw it (minimum) to freeze it when I catch it

Assume 1l of water, at 20C in toss, neglect Air resistance and temp gradient is linear

G on mars is 3.73 m/ss