You have N cards with different numbers on them. Your goal is to find a card with a maximal number. At the beginning all cards are put into the hat. You start getting them one by one and look at the numbers on them. After each card you can select it and stop the process. If it is really the card with the maximal number you win otherwise you lose. Also you can skip the current card and continue process. Fortunately you have a friend who helps with a good strategy: you pull X cards and memorize their values. Then you continue the process and select as answer the first card with value greater than the maximal value you memorized. Unfortunately you don't know the value of Xthat maximizes you chances of winning. Your task is to find X.

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <queue>
#include <iomanip>
#include <string>
#include <ctime>
#include <list>
typedef unsigned char byte;
#define pb push_back
#define input_fast std::ios::sync_with_stdio(false);std::cin.tie(0)
#define local freopen("in.txt","r",stdin)
#define pi acos(-1)using namespace std;
const int MAXN = 240;struct bign
{int len, s[MAXN];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[MAXN];sprintf(s, "%d", num);*this = s;return *this;}bign operator = (const char *num){for(int i = 0; num[i] == '0'; num++) ;  //去前导0len = strlen(num);for(int i = 0; i < len; i++) s[i] = num[len-i-1] - '0';return *this;}bign operator + (const bign &b) const //+
    {bign c;c.len = 0;for(int i = 0, g = 0; g || i < max(len, b.len); i++){int x = g;if(i < len) x += s[i];if(i < b.len) x += b.s[i];c.s[c.len++] = x % 10;g = x / 10;}return c;}bign operator += (const bign &b){*this = *this + b;return *this;}void clean(){while(len > 1 && !s[len-1]) len--;}bign operator * (const bign &b) //*
    {bign c;c.len = len + b.len;for(int i = 0; i < len; i++){for(int j = 0; j < b.len; j++){c.s[i+j] += s[i] * b.s[j];}}for(int i = 0; i < c.len; i++){c.s[i+1] += c.s[i]/10;c.s[i] %= 10;}c.clean();return c;}bign operator *= (const bign &b){*this = *this * b;return *this;}bign operator - (const bign &b){bign c;c.len = 0;for(int i = 0, g = 0; i < len; i++){int x = s[i] - g;if(i < b.len) x -= b.s[i];if(x >= 0) g = 0;else{g = 1;x += 10;}c.s[c.len++] = x;}c.clean();return c;}bign operator -= (const bign &b){*this = *this - b;return *this;}bign operator / (const bign &b){bign c, f = 0;for(int i = len-1; i >= 0; i--){f = f*10;f.s[0] = s[i];while(f >= b){f -= b;c.s[i]++;}}c.len = len;c.clean();return c;}bign operator /= (const bign &b){*this  = *this / b;return *this;}bign operator % (const bign &b){bign r = *this / b;r = *this - r*b;return r;}bign operator %= (const bign &b){*this = *this % b;return *this;}bool operator < (const bign &b){if(len != b.len) return len < b.len;for(int i = len-1; i >= 0; i--){if(s[i] != b.s[i]) return s[i] < b.s[i];}return false;}bool operator > (const bign &b){if(len != b.len) return len > b.len;for(int i = len-1; i >= 0; i--){if(s[i] != b.s[i]) return s[i] > b.s[i];}return false;}bool operator == (const bign &b){return !(*this > b) && !(*this < b);}bool operator != (const bign &b){return !(*this == b);}bool operator <= (const bign &b){return *this < b || *this == b;}bool operator >= (const bign &b){return *this > b || *this == b;}string str() const{string res = "";for(int i = 0; i < len; i++) res = char(s[i]+'0') + res;return res;}
};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;
}bign val[150];bign Caculate(int x,int y)
{bign res = 0;if (x == y && x == 1){bign rea  = 1;return rea;}if (x < y) return res;return val[x] / val[x-y];
}int main(int argc,char *argv[])
{val[0] = 1;freopen("out.txt","w",stdout);for(int i = 1 ; i <= 100 ; ++ i) val[i] = val[i-1] * i;for(int n = 5 ; n <= 100 ; ++ n){bign MAX = 0;int ans;bign check = 0;for(int x = 1 ; x <= n-1 ; ++ x){check = 0;for(int j = x + 1 ; j <= n ; ++ j)for(int t = x ; t <= n-1 ; ++ t){check = check +  Caculate(n-j,n-t-1) * Caculate(x,1) * Caculate(t-1,t-1);}if (check > MAX){MAX = check;ans = x;}}cout << "a[" << n <<"] = " << ans << ";" << endl;}return 0;
}

#include <iostream>
#include <cstring>
using namespace std;
int a[105];
long long f[70][70][2];int main()
{
memset(f,0,sizeof(f));a[5] = 2;
a[6] = 2;
a[7] = 2;
a[8] = 3;
a[9] = 3;
a[10] = 3;
a[11] = 4;
a[12] = 4;
a[13] = 5;
a[14] = 5;
a[15] = 5;
a[16] = 6;
a[17] = 6;
a[18] = 6;
a[19] = 7;
a[20] = 7;
a[21] = 8;
a[22] = 8;
a[23] = 8;
a[24] = 9;
a[25] = 9;
a[26] = 9;
a[27] = 10;
a[28] = 10;
a[29] = 10;
a[30] = 11;
a[31] = 11;
a[32] = 12;
a[33] = 12;
a[34] = 12;
a[35] = 13;
a[36] = 13;
a[37] = 13;
a[38] = 14;
a[39] = 14;
a[40] = 15;
a[41] = 15;
a[42] = 15;
a[43] = 16;
a[44] = 16;
a[45] = 16;
a[46] = 17;
a[47] = 17;
a[48] = 17;
a[49] = 18;
a[50] = 18;
a[51] = 19;
a[52] = 19;
a[53] = 19;
a[54] = 20;
a[55] = 20;
a[56] = 20;
a[57] = 21;
a[58] = 21;
a[59] = 22;
a[60] = 22;
a[61] = 22;
a[62] = 23;
a[63] = 23;
a[64] = 23;
a[65] = 24;
a[66] = 24;
a[67] = 24;
a[68] = 25;
a[69] = 25;
a[70] = 26;
a[71] = 26;
a[72] = 26;
a[73] = 27;
a[74] = 27;
a[75] = 27;
a[76] = 28;
a[77] = 28;
a[78] = 29;
a[79] = 29;
a[80] = 29;
a[81] = 30;
a[82] = 30;
a[83] = 30;
a[84] = 31;
a[85] = 31;
a[86] = 31;
a[87] = 32;
a[88] = 32;
a[89] = 33;
a[90] = 33;
a[91] = 33;
a[92] = 34;
a[93] = 34;
a[94] = 34;
a[95] = 35;
a[96] = 35;
a[97] = 35;
a[98] = 36;
a[99] = 36;
a[100] = 37;int n;cin >> n;cout << a[n] <<endl;return 0;
}