Split two peas in a pod

Probability Level 5

What is the smallest integer $N$ , such that no matter how we split the set $S_N = \{ 1, 2, \ldots, N \}$ into two sets $A$ and $B$ , there exists one set such that we can find 20 (not necessarily distinct) elements $x_1, x_2, \ldots x_{20}$ satisfying

$x_1 + x_2 + \ldots + x_{19} = x_{20}?$