Description

我们想明白递归函数到底是怎么运作的，所以想用递归来计算当给定一个正整数$n(n < 16)$时，求出$n + (n-1)……+1$的值,同时进行一些输出 要求写一个$int$ $plus1(int a)$形式的函数，在进入递归函数时，输出相关信息。在调用结束返回值前，输出相关信息。最后输出$n + (n-1)……+1$的值

Format

Input

3

Output

$[plus1(3) \space output]Begin \space invoke \space plus1(3)$

$[plus1(3) \space output]I \space want \space to \space calculate \space plus1(3), \space require \space 3 \space and \space the \space value \space of \space plus1(2), \space so \space I \space need \space to \space invoke \space plus1(2)$

$[plus1(2) \space output]Begin \space invoke \space plus1(2)$

$[plus1(2) \space output]I \space want \space to \space calculate \space plus1(2), \space require \space 2 \space and \space the \space value \space of \space plus1(1), \space so \space I \space need \space to \space invoke \space plus1(1)$

$[plus1(1) \space output]Begin \space invoke \space plus1(1)$

$[plus1(1) \space output]return \space plus1(1) \space = \space 1$

$[plus1(2) \space output]I \space got \space the \space value \space of \space plus1(1), \space and \space plus \space it \space to \space 2 \space then \space return3$

$[plus1(3) \space output]I \space got \space the \space value \space of \space plus1(2), \space and \space plus \space it \space to \space 3 \space then \space return \space 6$

$6$

Samples

3

[plus1(3) output]Begin invoke plus1(3)
[plus1(3) output]I want to calculate plus1(3), require 3 and the value of plus1(2),so I need to invoke plus1(2)
[plus1(2) output]Begin invoke plus1(2)
[plus1(2) output]I want to calculate plus1(2), require 2 and the value of plus1(1),so I need to invoke plus1(1)
[plus1(1) output]Begin invoke plus1(1)
[plus1(1) output]return plus1(1) = 1
[plus1(2) output]I got the value of plus1(1), and plus it to 2then return3
[plus1(3) output]I got the value of plus1(2), and plus it to 3then return6
6

Hints

int plus1(int a)
{
  // 从这里输出开始调用时的信息
  if(a == 1)
  {
    // 从这里输出最后一次调用的返回信息
    return ……;
  }
  else
  {
    // 从这里输出调用时的信息
    // 开始进行递归调用下一步
    ……
    int c = plus1(a - 1);
    // 从这里输出返回值前的信息
    ……
    return ……;
  }
}