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CSES - HIIT Open 2018

HIIT Open 2018

Contest start:2018-05-26 11:00:00
Contest end:2018-05-26 16:00:00

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Coins

Time limit:1.00 s
Memory limit:512 MB

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
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.