struct bign
{
    int len, s[numlen];
    bign()
    {
        memset(s, 0, sizeof(s));
        len = 1;
    }
    bign(int num)
    {
        *this = num;
    }
    bign(const char *num)
    {
        *this = num;
    }
    bign operator = (const int num)
    {
        char s[numlen];
        sprintf(s, 
 
"%d", num);
        *this = s;
        return *this;
    }
    bign operator = (const char *num)
    {
        len = strlen(num);
        while(len > 1 && num[0] == '0') num++, len--;
        for(int i = 0; i < len; i++) s[i] = num[len-i-1] - '0';
        return *this;
    }

    void deal()
    {
        
 
while(len > 1 && !s[len-1]) len--;
    }

    bign operator + (const bign &a) const
    {
        bign ret;
        ret.len = 0;
        int top = max(len, a.len), add = 0;
        for(int i = 0; add || i < top; i++)
        {
            int now = add;
            if(i < len) now += s[i];
            
 
if(i < a.len)   now += a.s[i];
            ret.s[ret.len++] = now%10;
            add = now/10;
        }
        return ret;
    }
    bign operator - (const bign &a) const
    {
        bign ret;
        ret.len = 0;
        int cal = 0;
        for(int i = 0; i < len; i++)
        {
            int now = s[i] - cal;
            if(i < a.len)   now -= a.s[i];
            if(now >= 0)    cal = 0;
            else
            {
                cal = 1;
                now += 10;
            }
            ret.s[ret.len++] = now;
        }
        ret.deal();
        return ret;
    }
    bign operator * (const bign &a) const
    {
        bign ret;
        ret.len = len + a.len;
        for(int i = 0; i < len; i++)
        {
            for(int j = 0; j < a.len; j++)
                ret.s[i+j] += s[i]*a.s[j];
        }
        for(int i = 0; i < ret.len; i++)
        {
            ret.s[i+1] += ret.s[i]/10;
            ret.s[i] %= 10;
        }
        ret.deal();
        return ret;
    }

    //乘以小數，直接乘快點
    bign operator * (const int num)
    {
        bign ret;
        ret.len = 0;
        int bb = 0;
        for(int i = 0; i < len; i++)
        {
            int now = bb + s[i]*num;
            ret.s[ret.len++] = now%10;
            bb = now/10;
        }
        while(bb)
        {
            ret.s[ret.len++] = bb % 10;
            bb /= 10;
        }
        ret.deal();
        return ret;
    }

    bign operator / (const bign &a) const
    {
        bign ret, cur = 0;
        ret.len = len;
        for(int i = len-1; i >= 0; i--)
        {
            cur = cur*10;
            cur.s[0] = s[i];
            while(cur >= a)
            {
                cur -= a;
                ret.s[i]++;
            }
        }
        ret.deal();
        return ret;
    }

    bign operator % (const bign &a) const
    {
        bign b = *this / a;
        return *this - b*a;
    }

    bign operator += (const bign &a)
    {
        *this = *this + a;
        return *this;
    }
    bign operator -= (const bign &a)
    {
        *this = *this - a;
        return *this;
    }
    bign operator *= (const bign &a)
    {
        *this = *this * a;
        return *this;
    }
    bign operator /= (const bign &a)
    {
        *this = *this / a;
        return *this;
    }
    bign operator %= (const bign &a)
    {
        *this = *this % a;
        return *this;
    }

    bool operator < (const bign &a) const
    {
        if(len != a.len)    return len < a.len;
        for(int i = len-1; i >= 0; i--) if(s[i] != a.s[i])
                return s[i] < a.s[i];
        return false;
    }
    bool operator > (const bign &a) const
    {
        return a < *this;
    }
    bool operator <= (const bign &a) const
    {
        return !(*this > a);
    }
    bool operator >= (const bign &a) const
    {
        return !(*this < a);
    }
    bool operator == (const bign &a) const
    {
        return !(*this > a || *this < a);
    }
    bool operator != (const bign &a) const
    {
        return *this > a || *this < a;
    }

    string str() const
    {
        string ret = "";
        for(int i = 0; i < len; i++) ret = char(s[i] + '0') + ret;
        return ret;
    }
};
istream& operator >> (istream &in, bign &x)
{
    string s;
    in >> s;
    x = s.c_str();
    return in;
}
ostream& operator << (ostream &out, const bign &x)
{
    out << x.str();
    return out;
}
// 大數開平方
bign Sqrt(bign x)
{
    int a[numlen/2];
    int top = 0;
    for(int i = 0; i < x.len; i += 2)
    {
        if(i == x.len-1)
        {
            a[top++] = x.s[i];
        }
        else
            a[top++] = x.s[i] + x.s[i+1]*10;
    }
    bign ret = (int)sqrt((double)a[top-1]);
    int xx = (int)sqrt((double)a[top-1]);
    bign pre = a[top-1] - xx*xx;
    bign cc;
    for(int i = top-2; i >= 0; i--)
    {
        pre = pre*100 + a[i];
        cc = ret*20;
        for(int j = 9; j >= 0; j--)
        {
            bign now = (cc + j)*j;
            if(now <= pre)
            {
                ret = ret*10 + j;
                pre -= now;
                break;
            }
        }
    }
    return ret;
}