Problem 1106 Sum of Factorials

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本文介绍了一个编程问题，任务是判断一个给定的非负整数是否可以表示为若干个阶乘数之和。通过预计算一系列阶乘值并利用这些值来检查目标数是否符合条件。

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Problem Description

John von Neumann, b. Dec. 28, 1903, d. Feb. 8, 1957, was a Hungarian-American mathematician who made important contributions to the foundations of mathematics, logic, quantum physics, meteorology, science, computers, and game theory. He was noted for a phenomenal memory and the speed with which he absorbed ideas and solved problems. In 1925 he received a B.S. diploma in chemical engineering from Zurich Institute and in 1926 a Ph.D. in mathematics from the University of Budapest. His Ph.D. dissertation on set theory was an important contribution to the subject. At the age of 20, von Neumann proposed a new definition of ordinal numbers that was universally adopted. While still in his twenties, he made many contributions in both pure and applied mathematics that established him as a mathematician of unusual depth. His Mathematical Foundations of Quantum Mechanics (1932) built a solid framework for the new scientific discipline. During this time he also proved the mini-max theorem of GAME THEORY. He gradually expanded his work in game theory, and with coauthor Oskar Morgenstern he wrote Theory of Games and Economic Behavior (1944).

There are some numbers which can be expressed by the sum of factorials. For example 9,9=1!+2!+3!. Dr. von Neumann was very interested in such numbers. So, he gives you a number n, and wants you to tell him whether or not the number can be expressed by the sum of some factorials.

Well, it's just a piece of cake. For a given n, you'll check if there are some xi, and let n equal to

If the answer is yes, say "YES"; otherwise, print out "NO".

Input

You will get several non-negative integer n (n <= 1,000,000) from input file. Each one is in a line by itself.

The input is terminated by a line with a negative integer.

Output

For each n, you should print exactly one word ("YES" or "NO") in a single line. No extra spaces are allowed.

Sample Input

-1

Sample Output

YES

题意：给出一个数n,验证n能不能由连续数字的阶乘和表示，注意的是0也要算进去，即0！+1！+2！=4是成立的

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
using namespace std;
int n;
int a[15];
int main()
{
    a[0] = 1;
    for(int i=1; i<15; i++)
    {
        a[i] = i * a[i-1];
    }
    while(~scanf("%d",&n)&&n>=0)
    {
        if(n==0)
        {
            printf("NO\n");
            continue;
        }
        for(int i=15-1; i>=0; i--)
        {
            if( n >= a[i] )
            {
                n -= a[i];
            }
        }
        printf(n==0?"YES\n":"NO\n");
    }
    return 0;
}