输入
2
10
9
43954713
输出
1
3
3
11
我的代码如下：结果可以输出来并且正确，但是提交到OJ上时却错误，这有可能是什么错误？

import java.util.*;

public class Main {
    public static int fun(int n) {
        int s = 1;
        for (int i = 1; i <= n; i++) {
            s *= i;
        }
        return s;
    }

    public static void main(String[] args) {
        Scanner cin = new Scanner(System.in);
        int a, sum = 0, n = 0;
        while (cin.hasNext()) {
            a = cin.nextInt();
            if (a == 0) {
                break;
            } else {
                for (; n <= a; n++) {
                    sum += fun(n);
                    if (sum >= a) {
                        break;
                    }
                }
                System.out.println(n);
            }
        }
    }
}

那单把 a 的类型改成 BigInteger，还要强制转成 int 么