Proof:
https://drive.google.com/file/d/1N2dT_-FDiUH1FcLrcFVJwynuDeVFt7pk/view?usp=sharing
https://drive.google.com/file/d/1u4bEIeJ-LUO-Gau6ON40nbxOjaGGm_r6/view?usp=sharing