The main idea is: dp[i][j] represent what is the maximum sum of two towers when the difference is j.
/***********Template Starts Here***********/
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include <functional>
#include <string>
#include <iostream>
#include <cctype>
#include <set>
#include <climits>
#include <iomanip>
#include <cassert>
//#include <unordered_map>
#define pb push_back
#define nl puts ("")
#define sp printf ( " " )
#define phl printf ( "hello\n" )
#define ff first
#define ss second
#define POPCOUNT __builtin_popcountll
#define RIGHTMOST __builtin_ctzll
#define LEFTMOST(x) (63-__builtin_clzll((x)))
#define MP make_pair
#define FOR(i,x,y) for(int i = (x) ; i <= (y) ; ++i)
#define ROF(i,x,y) for(int i = (y) ; i >= (x) ; --i)
#define CLR(x,y) memset(x,y,sizeof(x))
#define UNIQUE(V) (V).erase(unique((V).begin(),(V).end()),(V).end())
#define MIN(a,b) ((a)<(b)?(a):(b))
#define MAX(a,b) ((a)>(b)?(a):(b))
#define NUMDIGIT(x,y) (((int)(log10((x))/log10((y))))+1)
#define SQ(x) ((x)*(x))
#define ABS(x) ((x)<0?-(x):(x))
#define FABS(x) ((x)+eps<0?-(x):(x))
#define ALL(x) (x).begin(),(x).end()
#define LCM(x,y) (((x)/gcd((x),(y)))*(y))
#define SZ(x) ((int)(x).size())
#define NORM(x) if(x>=mod)x-=mod;
using namespace std;
typedef long long vlong;
typedef unsigned long long uvlong;
typedef pair < int, int > pii;
typedef pair < vlong, vlong > pll;
typedef vector<pii> vii;
typedef vector<int> vi;
const vlong inf = 2147383647;
const double pi = 2 * acos ( 0.0 );
const double eps = 1e-9;
#ifdef forthright48
#include <ctime>
clock_t tStart = clock();
#define debug(args...) {dbg,args; cerr<<endl;}
#define timeStamp printf("Execution Time: %.2fs\n", (double)(clock() - tStart)/CLOCKS_PER_SEC)
#else
#define debug(args...) // Just strip off all debug tokens
#define timeStamp
#endif
struct debugger{
template<typename T> debugger& operator , (const T& v){
cerr<<v<<" ";
return *this;
}
}dbg;
//int knightDir[8][2] = { {-2,1},{-1,2},{1,2},{2,1},{2,-1},{-1,-2},{1,-2},{-2,-1} };
//int dir4[4][2] = {{-1,0},{0,1},{1,0},{0,-1}};
inline vlong gcd ( vlong a, vlong b ) {
a = ABS ( a ); b = ABS ( b );
while ( b ) { a = a % b; swap ( a, b ); } return a;
}
vlong ext_gcd ( vlong A, vlong B, vlong *X, vlong *Y ){
vlong x2, y2, x1, y1, x, y, r2, r1, q, r;
x2 = 1; y2 = 0;
x1 = 0; y1 = 1;
for (r2 = A, r1 = B; r1 != 0; r2 = r1, r1 = r, x2 = x1, y2 = y1, x1 = x, y1 = y ) {
q = r2 / r1;
r = r2 % r1;
x = x2 - (q * x1);
y = y2 - (q * y1);
}
*X = x2; *Y = y2;
return r2;
}
inline vlong modInv ( vlong a, vlong m ) {
vlong x, y;
ext_gcd( a, m, &x, &y );
if ( x < 0 ) x += m; //modInv is never negative
return x;
}
inline vlong power ( vlong a, vlong p ) {
vlong res = 1, x = a;
while ( p ) {
if ( p & 1 ) res = ( res * x );
x = ( x * x ); p >>= 1;
}
return res;
}
inline vlong bigmod ( vlong a, vlong p, vlong m ) {
vlong res = 1 % m, x = a % m;
while ( p ) {
if ( p & 1 ) res = ( res * x ) % m;
x = ( x * x ) % m; p >>= 1;
}
return res;
}
/***********Template Ends Here***********/
/*********** Hasib Templates Starts Here**********/
#include<bits/stdc++.h>
using namespace std;
#define loop(i, n) for(int i=0; i<(n); i++)
#define sf scanf
#define pf printf
#define fr first
#define sc second
#define ll long long
#define dd double
#define all(v) (v).begin(), (v).end()
#define PI acos(-1.0)
#define mem(ara, val) memset(ara, val, sizeof(ara))
#define paii pair<int, int>
#define pall pair<ll, ll>
#define read(nm) freopen(nm, "r", stdin)
#define write(nm) freopen(nm, "w", stdout)
#define vdump(x) cerr<<#x<<" = "<<x<<endl;
#define dump(args...) cerr,args; cerr<<endl
template<typename T>
ostream& operator<<(ostream& out, vector<T> v)
{
out<<"[ ";
loop(i, SZ(v))
{
if(i) out<<", ";
out<<v[i];
}
out<<" ]";
return out;
}
template<typename T1, typename T2>
ostream& operator<<(ostream &out, pair<T1, T2> p)
{
out<<"( "<<p.fr<<", "<<p.sc<<")";
return out;
}
template<typename T>
ostream& operator,(ostream &out, T x)
{
out<<x<<" ";
return out;
}
/**********Hasib Templates Ends Here**************/
/**
* WARTNING for me:
* Never use FOR
* Never use pii, pll, vi, vi
* Never use ff, ss, phl, sp, nl
*/
#define MAXX 57
#define MAXSUM 500007
int ara[MAXX];
int N;
int dp[2][MAXSUM];
int solve()
{
mem(dp, -1);
dp[0][0] = 0;
int now, pre;
now = 1, pre = 0;
loop(i, N)
{
loop(j, MAXSUM)
{
if(dp[pre][j] != -1)
{
dp[now][j] = max(dp[now][j], dp[pre][j]);
int diff = abs(j - ara[i]);
dp[now][diff] = max(dp[now][diff], max(dp[pre][diff], dp[pre][ j ] + ara[i] ));
//pf("dp[%d] = %d\n", diff, dp[now][diff]);
diff = j + ara[i];
dp[now][diff] = max(dp[now][diff], max(dp[pre][diff], dp[pre][ j ] + ara[i] ));
//pf("dp[%d] = %d\n", diff, dp[now][diff]);
}
}
swap(now, pre);
}
return max(dp[now][0], dp[pre][0]);
}
int main ()
{
#ifdef hasibpc
read("input.txt");
//write("output.txt");
#endif // hasibpc
int kases, kaseno = 0;
sf("%d", &kases);
while(kases--)
{
sf("%d", &N);
loop(i, N)
{
sf("%d", &ara[i]);
}
sort(ara, ara+N); ///optimization ð
int ret = solve();
if(ret != 0)
{
pf("Case %d: %d\n",++kaseno, ret/2);
}
else
{
pf("Case %d: impossible\n", ++kaseno);
}
}
return 0;
}
, then there must be a divisor less than 
by multiplication. So, we only need to loop from 1 to 
UnLucky Codes 