Vova has invented a game with paper cups

Vova has invented a game with paper cups. He lines up 100 cups face down in a straight line from left to right and consecutively labels them from 1 to 100. Vova then walks from left to right down the line of cups, flipping all of the cups over. He returns to the left end of the line, then makes a second pass from left to right, this time flipping cups 2, 4, 6, 8 . . . . On the third pass, he flips cups 3, 6, 9, 12 . . .. He continues like this: On the i th pass, he flips over cups i, 2i, 3i, 4i, . . .. (By "flip," we mean changing the cup from face down to face up or vice versa.) After 100 passes, how many cups are face down?