Is methylchloride reaction with water SN1 or SN2

I wanted to know if methylchloride reacting with $ce{H2O}$ would be S_N1 or S_N2.

Methyl halide would not react using S_N1 because methyl carbocation is very unstable but it would also not react using S_N2 because $ce{H2O}$ is polar protic.

Please correct me if I am wrong. I think in this problem there would be no reaction. What are your opinions?