Interesting fun of Yura

In the computer science class, Yuri became very sad, so he came up with a game for himself.

At the beginning, he has an empty set. In each subsequent step, he thinks of a number and checks whether it belongs to the set. If the number belongs to the set, Yuri shouts "Yes". If not, he shouts "No" and adds it to the set. Before thinking of a new number, Yuri shouts the number of elements in the set.

The teacher got tired of Yuri's shouts, so he made him write a program that would shout instead of him. But Yuri doesn't know how to program, so he asked you for help.

Input

The first line contains one positive integer $n(1\le n\le 10^5)$. Each of the following $n$ lines contains an integer that Yuri has thought of. Yuri can only think of numbers in the range from $-10^9$ to $10^9$.

Output

On a separate line, print what Yuri would shout for each query.

Examples