Problem Description

题目描述

Astronauts have landed on a new planet, Kickstartos. They have discovered a machine on the planet: a generator that creates gold bars. The generator works as follows. On the first day, an astronaut inputs a positive integer $K$ into the generator. The generator will produce $K$ gold bars that day. The next day, it will produce $K + 1$, the following day, $K + 2$, and so on. Formally, on day $i$, the generator will produce $K + i - 1$ gold bars.

However, the astronauts also know that the generator will stop producing gold bars after it has produced a total of $G$ gold bars. They are curious about how many different positive integers $K$ could have been input into the generator.

Given $G$, find the number of different positive integers $K$ such that the generator will produce exactly $G$ gold bars before stopping.

Limits

$1 \le T \le 100$.

$1 \le G \le 10^{12}$.

输入格式

The first line of the input gives the number of test cases, $T$. $T$ lines follow.

Each line contains a single integer $G$, representing the maximum number of gold bars the generator can generate.

输出格式

For each test case, output one line containing Case #$x$: followed by $y$, where $x$ is the test case number (starting from $1$) and $y$ is the number of possible values of $K$ on day $1$ that would eventually produce exactly $G$ gold bars.

样例

样例 1

提示

For Sample Case #$1$, there are $2$ possible values of $K$ ($1$, $10$) that would eventually produce exactly $10$ gold bars. For $K = 1$, we will have $1 + 2 + 3 + 4 = 10$ gold bars after $4$ days, and for $K = 10$, we will have $10$ gold bars after just $1$ day.

For Sample Case #$2$, there are $4$ possible values of $K$ ($8$, $23$, $62$, $125$) that would eventually produce exactly $125$ gold bars.

2
10
125

Case #1: 2
Case #2: 4