Stack Weights

You have n coins, each of which has a distinct weight. There are two stacks which are initially empty. On each step you move one coin to a stack. You never remove a coin from a stack. After each move, your task is to determine which stack is heavier (if we can be sure that either stack is heavier).

Input

The first input line has an integer n: the number of coins. The coins are numbered 1,2,\dots,n. You know that coin i is always heavier than coin i-1, but you don't know their exact weights. After this, there are n lines that describe the moves. Each line has two integers c and s: move coin c to stack s (1 = left, 2 = right).

Output

After each move, print < if the right stack is heavier, > if the left stack is heavier, and ? if we can't know which stack is heavier.

Constraints

$1 \le n \le 2$ \cdot 10^5$

Example

Input

3
2 1
3 2
1 1

Output

>
<
?

Explanation: After the last move, if the coins are [2,3,4], the left stack is heavier, but if the coins are [1,2,5], the right stack is heavier.