Your colleague tells you that the short butterfly strategy can also be implemented using only put options (short put butterfly): short 1 put option with strike price K1, long 2 put options with strike price K2, and short 1 put option with strike price K3 where K1 < K2 < K3 and 2K2 = K1 + K3. Assuming no bid-ask spread or transaction cost, does the short call butterfly and the short put butterfly have the same initial cost? Prove your claim.