# Light OJ: 1401 – No More Tic-tac-toe / UVa 11534 – Say Goodbye to Tic-Tac-Toe

0

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=2529

http://www.lightoj.com/volume_showproblem.php?problem=1401

Solutiono Idea: Straight Forward Grundy theory. Think a gap as a nim pile.

```
#include &lt;bits/stdc++.h&gt;
//#include &lt;ext/pb_ds/assoc_container.hpp&gt;
//#include &lt;ext/pb_ds/tree_policy.hpp&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cerr&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;

//using namespace __gnu_pbds;
//typedef tree&lt;int, null_type, less&lt;int&gt;, rb_tree_tag, tree_order_statistics_node_update&gt; ordered_set;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//int Set(int N,int pos){return N=N | (1&lt;&lt;pos);}
//int reset(int N,int pos){return N= N &amp; ~(1&lt;&lt;pos);}
//bool check(int N,int pos){return (bool)(N &amp; (1&lt;&lt;pos));}
/*------------------------------------------------*/

char str[201];

int dp[102][3][3];

int grundy(int len, int lft, int rgt)
{
if(len&lt;=0) return 0;
if(len==1 &amp;&amp; lft==rgt &amp;&amp; lft!=2) return 1;
if(len==1 &amp;&amp; lft!=rgt &amp;&amp; lft!=2 &amp;&amp; rgt!=2 ) return 0;
int &amp;ret=dp[len][lft][rgt];
if(ret!=-1) return ret;
set&lt;int&gt;st;
for(int i=1; i&lt;=len; i++)
{
int a=0,b=0;
if(i==1)
{
if(lft!=0)
{a=grundy(i-1,lft,0)^grundy(len-i,0,rgt);st.insert(a);}
if(lft!=1)
{b=grundy(i-1,lft,1)^grundy(len-i,1,rgt);st.insert(b);}
}
else if(i==len)
{
if(rgt!=0)
{a=grundy(i-1,lft,0)^grundy(len-i,0,rgt);st.insert(a);}
if(rgt!=1)
{b=grundy(i-1,lft,1)^grundy(len-i,1,rgt);st.insert(b);}
}
else
{
a=grundy(i-1,lft,0)^grundy(len-i,0,rgt);
b=grundy(i-1,lft,1)^grundy(len-i,1,rgt);
st.insert(a);
st.insert(b);
}
}

int x=0;
while(st.find(x)!=st.end()) x++;
return ret=x;
}

int main()
{

//    freopen(&quot;in.txt&quot;,&quot;r&quot;,stdin);
//	  freopen(&quot;out.txt&quot;,&quot;w&quot;,stdout);

int t;
sf(t);
ms(dp,-1);
TEST_CASE(t)
{
scanf(&quot; %s&quot;,str);
int ans=0;
int len=strlen(str);
int last=-1;
for(int i=0; i&lt;len; i++)
{
if(str[i]!='.')
{
if(str[i]=='O')
{
ans^=grundy(i-last-1,2,0);
}
else
{
ans^=grundy(i-last-1,2,1);
}
last=i;
break;
}
}

for(int i=last+1; i&lt;len; i++)
{
if(str[i]!='.')
{
if(str[i]=='O')
{
ans^=grundy(i-last-1,str[last]=='X',0);
}
else
{
ans^=grundy(i-last-1,str[last]=='X',1);
}
last=i;
}
}
if(last==-1)
ans^=grundy(len-last-1,2,2);
else
ans^=grundy(len-last-1,str[last]=='X',2);

//        PRINT_CASE;

int cnt=0;
for(int i=0; i&lt;len; i++) cnt+=(str[i]!='.');
if(cnt%2==0)
{

if(ans)
printf(&quot;Possible.\n&quot;);
else
printf(&quot;Impossible.\n&quot;);
}
else
{
if(ans==0)
printf(&quot;Possible.\n&quot;);
else
printf(&quot;Impossible.\n&quot;);
}
}

return 0;
}

```

# Light OJ 1229 – TREBLECROSS / UVa 10561 – Treblecross

0

https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=1502

http://www.lightoj.com/volume_showproblem.php?problem=1229

```
#include &lt;bits/stdc++.h&gt;
//#include &lt;ext/pb_ds/assoc_container.hpp&gt;
//#include &lt;ext/pb_ds/tree_policy.hpp&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cerr&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;

//using namespace __gnu_pbds;
//typedef tree&lt;int, null_type, less&lt;int&gt;, rb_tree_tag, tree_order_statistics_node_update&gt; ordered_set;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//int Set(int N,int pos){return N=N | (1&lt;&lt;pos);}
//int reset(int N,int pos){return N= N &amp; ~(1&lt;&lt;pos);}
//bool check(int N,int pos){return (bool)(N &amp; (1&lt;&lt;pos));}
/*------------------------------------------------*/

//char str[400];

string str;

int dp[205];

int func(int m)
{
if(m&lt;=0) return 0;
int &amp;ret=dp[m];
if(ret!=-1) return ret;
set&lt;int&gt;st;
for(int i=1;i&lt;=m; i++)
{
st.insert(func(i-3)^func(m-i-2));
}
int x=0;
while(st.find(x)!=st.end())x++;
return ret=x;
}

bool solve(int idx)
{
if(str[idx]=='X') return 0;
string temp=str;
temp[idx]='X';
for(int i=0;i&lt;SZ(temp)-2;i++)
{
if(temp[i]=='X' &amp;&amp; temp[i+1]=='X' &amp;&amp; temp[i+2]=='X') return 1;
}
for(int i=0;i&lt;SZ(temp)-2;i++)
{
if(temp[i]=='X' &amp;&amp; temp[i+2]=='X') return 0;
}
for(int i=0;i&lt;SZ(temp)-1;i++)
{
if(temp[i]=='X' &amp;&amp; temp[i+1]=='X') return 0;
}

int ans=0,last=-1;
for(int i=0;i&lt;SZ(temp);i++)
{
if(temp[i]=='X')
{
if(last==-1)
ans^=func(i-last-3);
else
ans^=func(i-last-5);
last=i;
}
}
ans^=func(SZ(temp)-last-3);
return ans==0;
}

int main()
{
CIN;
//    freopen(&quot;in.txt&quot;,&quot;r&quot;,stdin);
//    freopen(&quot;out.txt&quot;,&quot;w&quot;,stdout);

int t;
//    sf(t);
cin&gt;&gt;t;
ms(dp,-1);
TEST_CASE(t)
{
cin&gt;&gt;str;
vector&lt;int&gt;pos;
for(int i=0;i&lt;SZ(str);i++)
{
if(solve(i))
{
pos.pb(i+1);
}
}
CASE_PRINT;
if(SZ(pos)==0)
cout&lt;&lt;0&lt;&lt;endl;
else
{
cout&lt;&lt;pos[0];
for(int i=1;i&lt;SZ(pos);i++)
cout&lt;&lt;&quot; &quot;&lt;&lt;pos[i];
cout&lt;&lt;endl;
}
}

return 0;
}

```

# Light OJ: 1315 – Game of Hyper Knights

0

```
#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//int Set(int N,int pos){return N=N | (1&lt;&lt;pos);}
//int reset(int N,int pos){return N= N &amp; ~(1&lt;&lt;pos);}
//bool check(int N,int pos){return (bool)(N &amp; (1&lt;&lt;pos));}
/*------------------------------------------------*/

int fx[]= {-2,-3,-2,-1,-1,+1};
int fy[]= {+1,-1,-1,-2,-3,-2};

int dp[2003][2003];

inline bool valid(int x,int y)
{
if(x&lt;0 || y&lt;0) return 0;
return 1;
}

int func(int x, int y)
{
int &amp;ret=dp[x][y];
if(ret!=-1) return ret;

int cnt=0;
for(int i=0; i&lt;6; i++)
cnt+=valid(x+fx[i],y+fy[i]);
if(cnt==0) return ret=0;

set&lt;int&gt;st;

for(int i=0; i&lt;6; i++)
{
if(valid(x+fx[i],y+fy[i]))
st.insert(func(x+fx[i],y+fy[i]));
}

int p=0;

while(st.find(p)!=st.end()) p++;
return ret=p;
}

int main()
{

//    freopen(&quot;in.txt&quot;,&quot;r&quot;,stdin);
///freopen(&quot;out.txt&quot;,&quot;w&quot;,stdout);

int t;
sf(t);

ms(dp,-1);

TEST_CASE(t)
{
int n;
sf(n);

int ans=0;

for(int i=0; i&lt;n; i++)
{
int a,b;
sff(a,b);
ans^=func(a,b);
}

PRINT_CASE;
if(ans)
{
pf(&quot;Alice\n&quot;);
}
else
pf(&quot;Bob\n&quot;);

}

return 0;
}

```

# Light OJ : 1296 – Again Stone Game

0

Solution Idea: Just Find the pattern for smaller input and get AC ðŸ˜›

```

#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//int Set(int N,int pos){return N=N | (1&lt;&lt;pos);}
//int reset(int N,int pos){return N= N &amp; ~(1&lt;&lt;pos);}
//bool check(int N,int pos){return (bool)(N &amp; (1&lt;&lt;pos));}
/*------------------------------------------------*/

int main()
{

///freopen(&quot;in.txt&quot;,&quot;r&quot;,stdin);
///freopen(&quot;out.txt&quot;,&quot;w&quot;,stdout);

int t;
sf(t);
TEST_CASE(t)
{
int n;
sf(n);

int ans=0;

for(int i=0;i&lt;n;i++)
{
int a;
sf(a);
while(a%2)
{
a/=2;
}
ans^=a/2;
}

PRINT_CASE;
if(ans)
pf(&quot;Alice\n&quot;);
else
pf(&quot;Bob\n&quot;);

}

return 0;
}

```

# Light OJ: 1199 – Partitioning Game

0

```
#include &lt;bits/stdc++.h&gt;

#define pii              pair &lt;int,int&gt;
#define pll              pair &lt;long long,long long&gt;
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI               vector &lt;int&gt;
#define DBG              pf(&quot;Hi\n&quot;)
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf(&quot;%d&quot;,&amp;a)
#define sfl(a)           scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)         scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)        scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)      scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)     scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i&lt;n;i++)
#define loop1(i,n)       for(int i=1;i&lt;=n;i++)
#define REP(i,a,b)       for(int i=a;i&lt;b;i++)
#define RREP(i,a,b)      for(int i=a;i&gt;=b;i--)
#define TEST_CASE(t)     for(int z=1;z&lt;=t;z++)
#define PRINT_CASE       printf(&quot;Case %d: &quot;,z)
#define LINE_PRINT_CASE  printf(&quot;Case %d:\n&quot;,z)
#define CASE_PRINT       cout&lt;&lt;&quot;Case &quot;&lt;&lt;z&lt;&lt;&quot;: &quot;
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1&lt;&lt;28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//int Set(int N,int pos){return N=N | (1&lt;&lt;pos);}
//int reset(int N,int pos){return N= N &amp; ~(1&lt;&lt;pos);}
//bool check(int N,int pos){return (bool)(N &amp; (1&lt;&lt;pos));}
/*------------------------------------------------*/

int dp[10005];

int func(int n)
{
if(n==1 || n==2) return 0;

if(dp[n]!=-1) return dp[n];

set&lt;int&gt;st;

int mid=n/2;
if(n%2==0) mid--;

for(int i=1;i&lt;=mid;i++)
{
st.insert(func(i)^func(n-i));
}

int ret=0;
while(st.find(ret)!=st.end()) ret++;
return dp[n]=ret;
}

int main()
{

///freopen(&quot;in.txt&quot;,&quot;r&quot;,stdin);
///freopen(&quot;out.txt&quot;,&quot;w&quot;,stdout);

ms(dp,-1);

int t;
sf(t);
TEST_CASE(t)
{
int n;
sf(n);

int ans=0;

for(int i=0;i&lt;n;i++)
{
int a;
sf(a);
ans^=func(a);
}

PRINT_CASE;

if(ans)
pf(&quot;Alice\n&quot;);
else
pf(&quot;Bob\n&quot;);

}

return 0;
}

```