Background

To check his teaching skills, Ysuperman decided to give two placement tests to kindergarten kids.

Problem Description

One test has four problems, with a total score of $400$; the other test has six problems, with a total score of $600$. For each person, the score in each test is a non-negative integer between $0$ and the full score (it can be $0$ or the full score).

There are $n$ students taking these two tests. For student $i$, the score of the first test is $a_i$, and the score of the second test is $b_i$. Ysuperman computes the standard score $c_i$ using the following rules:

1. Compute the highest scores of the two tests, $A, B$, with $A \ne 0$ and $B \ne 0$.
2. Let $c_i = 1000(\frac{a_i}{A}+\frac{b_i}{B})$, where $c_i$ is rounded to the nearest integer.

After computing every student's standard score, Ysuperman carelessly lost all the original scores. Can you help find any possible set of original scores?

In other words, given $n$ and the standard scores $c_{1\sim n}$, you need to find a valid set of $a_{1\sim n}$ and $b_{1\sim n}$ satisfying the requirements above.

In particular, there is a very strong kid, Qiu, who got the highest score in both tests, so it is guaranteed that $c_1 = 2000$. Also, the other kids are at a similar level, so it is guaranteed that $\forall i>1, c_i \in [10,1990]$.

Input Format

The first line contains a positive integer $n$.

The next $n$ lines each contain a positive integer $c_i$ on line $i$.

Output Format

Output $n$ lines. On line $i$, output two non-negative integers $a_i, b_i$. From the statement, you must ensure $a_i \in [0,400]$, $b_i \in [0,600]$, and $\max a_i > 0$, $\max b_i > 0$.

4
2000
1319
1476
996

233 525
147 361
200 324
0 523

4
2000
1704
1658
1542

400 454
352 374
352 353
320 337

Hint

In Sample 1, the constructed $a, b$ are valid for the following reasons:

The highest scores of the two tests are $233$ and $525$, respectively.

$1000\times (233\div 233 + 525\div 525)=2000$.

$1000\times (147\div 233 + 361\div 525) \approx 1318.520\approx 1319$.

$1000\times (200\div 233 + 324\div 525)\approx 1475.512\approx 1476$.

$1000\times (0\div 233 + 523\div 525)\approx 996.190\approx 996$.

For the first $20\%$ of the testdata, it is guaranteed that $n \le 20$.

For another $20\%$ of the testdata, it is guaranteed that $c_i$ is a multiple of $10$.

For another $20\%$ of the testdata, it is guaranteed that $c_i$ is a multiple of $5$.

For another $20\%$ of the testdata, it is guaranteed that $c_i$ is a multiple of $2$.

For $100\%$ of the testdata, $1 \le n \le 10^4$, $c_1 = 2000$, and $\forall i>1, c_i \in [10,1990]$.

Translated by ChatGPT 5