[JEE Main 2016] if the coefficient of x 2 in 1 x 2 1 x 3 1

If the coefficient of $x^2$ in $(1+x)^2+(1+x)^3+\cdots+(1+x)^{49}+(1+mx)^{50}$ is $(3n+1)\binom{51}3$ (for a positive integer $n$, $m$ the smallest positive integer making this hold), then $n=$ ____