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Codeforces Round 634 (Div. 3) |
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Finished |

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A. Candies and Two Sisters

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are two sisters Alice and Betty. You have $$$n$$$ candies. You want to distribute these $$$n$$$ candies between two sisters in such a way that:

- Alice will get $$$a$$$ ($$$a > 0$$$) candies;
- Betty will get $$$b$$$ ($$$b > 0$$$) candies;
- each sister will get some integer number of candies;
- Alice will get a greater amount of candies than Betty (i.e. $$$a > b$$$);
- all the candies will be given to one of two sisters (i.e. $$$a+b=n$$$).

Your task is to calculate the number of ways to distribute exactly $$$n$$$ candies between sisters in a way described above. Candies are indistinguishable.

Formally, find the number of ways to represent $$$n$$$ as the sum of $$$n=a+b$$$, where $$$a$$$ and $$$b$$$ are positive integers and $$$a>b$$$.

You have to answer $$$t$$$ independent test cases.

Input

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Then $$$t$$$ test cases follow.

The only line of a test case contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^9$$$) — the number of candies you have.

Output

For each test case, print the answer — the number of ways to distribute exactly $$$n$$$ candies between two sisters in a way described in the problem statement. If there is no way to satisfy all the conditions, print $$$0$$$.

Example

Input

6 7 1 2 3 2000000000 763243547

Output

3 0 0 1 999999999 381621773

Note

For the test case of the example, the $$$3$$$ possible ways to distribute candies are:

- $$$a=6$$$, $$$b=1$$$;
- $$$a=5$$$, $$$b=2$$$;
- $$$a=4$$$, $$$b=3$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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