Double Trouble

Alice has 𝑁 magical balls placed on the 𝑥-axis. The 𝑖-th ball is initially at position 𝑋𝑖​ and has a power of 𝑃𝑖​.

It is guaranteed that 𝑋𝑖<𝑋𝑖+1​ for 1≤𝑖<𝑁.

Initially, none of the balls are activated.

Alice can do the following at most twice:

• Choose an index i (1≤𝑖≤𝑁) such that ball 𝑖 is not activated.
• Activate ball 𝑖, and choose a direction for it (either right or left).

When ball 𝑖 is activated in a certain direction, the following process takes place:

• The ball will move 𝑃𝑖 units in the chosen direction.
• If, while moving, it strikes another ball 𝑗, ball 𝑖 will immediately disappear. Then,
• If ball j was previously activated, nothing happens, and the process immediately ends.
• Otherwise, ball j activates in the same direction as ball i (that is, if ball i was moving left, ball j will move left too).
• Note that the power of ball j doesn't change, and remains 𝑃𝑗.
• If it never strikes another ball, it simply stops after moving a distance of 𝑃𝑖 units.
• In this case, the ball does not disappear.

Using at most two moves, is it possible for Alice to activate every ball?

Note that Alice can make her second move only after the entire process from the first move has completed.