Timus : 1149 (Sinus Dances)



// http://acm.timus.ru/problem.aspx?space=1&num=1149
// Runtime: 0.046s
// Tag: Recursive 


// @BEGIN_OF_SOURCE_CODE

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <cctype>
#include <stack>
#include <queue>
#include <list>
#include <vector>
#include <map>
#include <sstream>
#include <cmath>
#include <bitset>
#include <utility>
#include <set>
#include <numeric>

#define INF_MAX 2147483647
#define INF_MIN -2147483647
#define pi acos(-1.0)
#define N 1000
#define LL long long

#define For(i, a, b) for( int i = (a); i < (b); i++ )
#define Fors(i, sz) for( size_t i = 0; i < sz.size (); i++ )
#define Fore(it, x) for(typeof (x.begin()) it = x.begin(); it != x.end (); it++)
#define Set(a, s) memset(a, s, sizeof (a))
#define Read(r) freopen(r, "r", stdin)
#define Write(w) freopen(w, "w", stdout)

using namespace std;

string saveAn [200 + 5];
int n;

string valueOf (int p)
{
    char a [10];
    sprintf (a, "%d", p);
    return a;
}

string An (int p, int k)
{
    if ( p == k ) return "sin(" + valueOf(p) + ")";
    string s = p % 2 == 0 ? "+" : "-";
    return "sin(" + valueOf(p) + s + An (p + 1, k) + ")";
}

string Sn (int p, int k) {
    if ( p == 1 ) return saveAn [p] + "+" + valueOf(k);
    return "(" + Sn (p - 1, k + 1) + ")" + saveAn [p] + "+" + valueOf(k);
}

int main ()
{
    for ( int i = 1; i <= 200; i++ ) saveAn [i] = An (1, i);

    while ( scanf ("%d", &n ) != EOF )
        cout << Sn (n, 1) << endl;

	return 0;
}

// @END_OF_SOURCE_CODE
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