#!/usr/bin/ruby def gen_odd(n) m=n.times.map{[0]*n} r=n-1 c=n/2 i=0 n.times{ r=(r+1)%n m[r][c]=i+=1 (n-1).times{ r=(r+n-1)%n c=(c+1)%n m[r][c]=i+=1 } } m end def gen_quad(n) z=n**2 i=0 m=n.times.map{[0]*n} n.times{|r|n.times{|c| j,k=i.divmod(n) j%=4 k%=4 m[r][c]=i+=1 m[r][c]=z-m[r][c]+1 if (j==0||j==3)&&(k==1||k==2) or (j==1||j==2)&&(k==0||k==3) }} m end def gen_lux(n) m=n.times.map{[0]*n} o={l:[[4,1],[2,3]],u:[[1,4],[2,3]],x:[[1,4],[3,2]]} lux=(n/4+1).times.map{[:l]*(n/2)} + [[:u]*(n/2)] + (n/4-1).times.map{[:x]*(n/2)} lux[n/4][n/4],lux[n/4+1][n/4]=lux[n/4+1][n/4],lux[n/4][n/4] b=gen_odd(n/2).map{|e|e.map{|f|4*(f-1)}} n.times{|r|n.times{|c| br,xr=r.divmod(2) bc,xc=c.divmod(2) m[r][c]=b[br][bc]+o[lux[br][bc]][xr][xc] }} m end def gen_magicsquare(n) if n%2==1 gen_odd(n) elsif n%4==0 gen_quad(n) else gen_lux(n) end end def sliding_parity(m) flat=[] n=m.size parity=0 n.times{|y|n.times{|x| k=m[y][x] if k!=n*n flat<flat[j] } } parity%2 end N=gets.to_i a=$<.map{|e| e.split.map{|f|f.to_i==0 ? N*N : f.to_i} } if N==2 puts :impossible exit end board=gen_magicsquare(N) if sliding_parity(a)!=sliding_parity(board) if N%2==0 board.reverse! else board[0],board[N-1]=board[N-1],board[0] end end puts :possible puts board.map{|e|e*' '}