Grammy joined a great party.

There is an interesting game at the party. There are piles of stones on the table. The -th pile has stones in it. Two players participate in the game and operate the stones in turn.

In each player's turn, the player will do the following two steps:

• Select a non-empty pile of stones, select a positive amount of stones to remove from it.
• Keep the remaining stones in the pile still or merge them all into another non-empty pile of stones.

Those who cannot operate lose the game.

Now, Grammy has questions. For each question, she asks you how many sub-segments of satisfy that if the piles in the segment are taken out alone for the game, the first player will win.