2014
11-27

# Simple Puzzle

Alpc83 is proud of his IQ, so he usually try to challenge the puzzle which is famous but more difficult than what we have known. Some days ago, he played the eight digits puzzle, and he thought it’s so easy. Then he want to challenge a N*N-1 digits puzzle whose rules are same with the eight digits puzzle. Firstly he have all the numbers from 0 to N*N-1 arranged in N rows and N columns randomly. Because he don’t want to waste time, he hope to make sure whether he can finally solve the puzzle if he is clever enough. Now he ask you for help.
(Ps. Don’t you know the eight digits puzzle? Oh, my god! Let me tell you: you have all numbers from 0 to 8 arranged in 3 rows and 3 columns. You are allowed to switch two adjacent elements (horizontally or vertically), only if one of them has the value 0. You have to decide whether there exists a sequence of moves which brings the puzzle in the initial state into the final state.)
In this puzzle , we will give you a initial state, and we set the final state is:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 0
(n=4 for example)

Each case starts with a line contains the integer N.
The following N lines describe the initial state, each of them containing n integers, describing the initial state of the puzzle.
A line with N = 0 indicates the end of the input; do not write any output for this case. (N<=300)

Each case starts with a line contains the integer N.
The following N lines describe the initial state, each of them containing n integers, describing the initial state of the puzzle.
A line with N = 0 indicates the end of the input; do not write any output for this case. (N<=300)

2
2 1
3 0
0

NO

#include<cstdio>
#include<cstdlib>
#include<cctype>
#include<cstring>
#include<cmath>
#include<ctime>
#include<vector>
#include<map>
#include<set>
#include<sstream>
#include<list>
#include<deque>
#include<stack>
#include<bitset>
#include<functional>
#include<numeric>
#include<utility>
#include<sstream>
#include<iomanip>
#include<algorithm>
#include<limits>
#include<iostream>
#include<fstream>
#include<string.h>
#include<string>
#include<queue>
using namespace std;
#define max(a,b) ((a>b)?a:b) //finding max
#define min(a,b) ((a<b)?a:b) //finding min
#define Max(a,b,c) max(a,max(b,c)) //finding max between 3 numbers
#define Min(a,b,c) min(a,min(b,c)) //finding min between 3 numbers
#define Pi acos(-1.0) //defining Pi for mathematical uses
#define Clear(a) memset(a,0,sizeof(a)) //clearing memory of an array
#define setfalse(a) memset(a,false,sizeof(a)) //setting the array into false
#define settrue(a) memset(a,true,sizeof(a)) //setting the array into true
#define clrstr(a) memset(a,'\0',sizeof(a)) //setting string array to null
#define open freopen("input.txt","r",stdin) //opening input file
#define close freopen ("output.txt","w",stdout) //opening output file
#define Case(a) printf("Case %d: ",a) //printing case number
#define caseh(a) printf("Case #%d: ",a) //printing case number having '#'
#define getcase(a) scanf("%d",&a) //scanning case number
#define caseloop(a,b) for(a=1;a<=b;a++) //making case loop
#define EPS 1e-9 //small value for avoiding preccesion error
#define LL long long //__int64 //long long short form
#define MX 50000 //MAX size/value
#define PB(x) push_back(x) //push in vector/string
#define PP pop_back() //pop from vector
#define PF(x) push_front(x) //push in vector/string/deque from front
#define PPF(x) pop_front() //pop from vector/deque from front
#define IN(x) insert(x) //insert element in set
#define PS(x) push(wax) //push element in stack/queue
#define P(x) pop() //pop element from stack/queue
template<class T>inline void checkmin(T &a,T b)
{
if(b<a)a=b;
}
template<class T>inline void checkmax(T &a,T b)
{
if(b>a)a=b;
}
const double eps=1e-11;
const double pi=acos(-1.0);
#define two(X) (1<<(X))
#define twoL(X) (((int64)(1))<<(X))
#define contain(S,X) (((S)&two(X))!=0)
#define containm(S,X) (((S)&twoL(X))!=0)
#define SIZE(A) ((int)A.size())
#define LENGTH(A) ((int)A.length())
#define MP(A,B) make_pair(A,B)
#define MUL(a,b) (int)(((int64)a*b%MOD))
#define FOR(i,a,b) for(i=(a);i<(b);i++)
#define REP(i,n) for(int i=0;i<(n);i++)
typedef pair<int,int>ipair;
#define MOD (1000000007)
const int size=305;
int a[size*size],id,res,c[size*size];
void res_ord(int l,int r)
{
int mid,i,j,tmp;
if(r>l+1)
{
mid=(l+r)/2;//
res_ord(l,mid);
res_ord(mid,r);
tmp=l;
for(i=l,j=mid; i<mid&&j<r;)
{
if(a[i]>a[j])
{
c[tmp++]=a[j++];
res+=mid-i;
}
else
c[tmp++]=a[i++];
}
if(j<r)
{
for(; j<r; j++)
c[tmp++]=a[j];
}
else
{
for(; i<mid; i++)
c[tmp++]=a[i];
}
for(i=l; i<r; i++)
a[i]=c[i];
}
}
int main()
{
int i,j,n,zero;
while(cin>>n,n)
{
id=res=0;
for(i=0; i<n; i++)
for(j=0; j<n; j++)
{
scanf("%d",&a[id]);
if(a[id]==0)
zero=i;
else
id++;
}
zero=n-1-zero;
res_ord(0,id);
if((n&1)==0)
{
//cout<<"fuck"<<endl;
if((((zero&1)==1)&&((res&1)==1))||
(((zero&1)==0)&&((res&1)==0))){

//cout<<res<<endl;
//cout<<zero<<endl;
cout<<"YES"<<endl;
}
else
cout<<"NO"<<endl;
}
else
{
//cout<<(n&1)<<" ---- "<<endl;
if(res&1)
cout<<"NO"<<endl;
else
cout<<"YES"<<endl;
}
}
return 0;
}

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