You are given an array $$$a$$$, consisting of $$$n$$$ integers (numbered from $$$1$$$ to $$$n$$$). Initially, they are all zeroes.

You have to process $$$q$$$ queries. The $$$i$$$-th query consists of two different integers $$$x_i$$$ and $$$y_i$$$. During the $$$i$$$-th query, you have to choose an integer $$$p$$$ (which is either $$$x_i$$$ or $$$y_i$$$) and an integer $$$d$$$ (which is either $$$1$$$ or $$$-1$$$), and assign $$$a_p = a_p + d$$$.

After each query, every element of $$$a$$$ should be a non-negative integer.

Process all queries in such a way that the sum of all elements of $$$a$$$ after the last query is the minimum possible.

Input format:
The first line contains two integers $$$n$$$ and $$$q$$$ ($$$2 \le n \le 3 \cdot 10^5$$$; $$$1 \le q \le 3 \cdot 10^5$$$) — the number of elements in $$$a$$$ and the number of queries, respectively.

Then $$$q$$$ lines follow. The $$$i$$$-th of these lines contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \le x_i, y_i \le n$$$; $$$x_i \ne y_i$$$) — the description of the $$$i$$$-th query.
Output format:
For each query, print a line containing two characters:

- the first character should be x if you choose $$$p=x_i$$$, or y if you choose $$$p=y_i$$$;
- the second character should be + if you choose $$$d=1$$$, or - if you choose $$$d=-1$$$.

If there are multiple answers, print any of them.
Example Input 0:
3 4
1 2
3 2
3 1
1 2

Example Output 0:
y+
x+
x-
y-

Example Input 1:
4 4
1 2
2 3
3 4
3 2

Example Output 1:
y+
y+
x-
y-

Example Input 2:
4 2
2 1
4 3

Example Output 2:
y+
x+



Example input:
3 4
1 2
3 2
3 1
1 2

4 4
1 2
2 3
3 4
3 2

4 2
2 1
4 3


Example output:
y+
x+
x-
y-

y+
y+
x-
y-

y+
x+