Andi and Budi were given an assignment to tidy up their bookshelf of n books. Each book is represented by the book title — a string s_i numbered from 1 to n, each with length m. Andi really wants to sort the book lexicographically ascending, while Budi wants to sort it lexicographically descending.

Settling their fight, they decided to combine their idea and sort it asc-desc-endingly, where the odd-indexed characters will be compared ascendingly, and the even-indexed characters will be compared descendingly.

A string a occurs before a string b in asc-desc-ending order if and only if in the first position where a and b differ, the following holds:

  * if it is an odd position, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b; 
  * if it is an even position, the string a has a letter that appears later in the alphabet than the corresponding letter in b. 

Input

The first line contains two integers n and m (1 ≤ n ⋅ m ≤ 10^6).

The i-th of the next n lines contains a string s_i consisting of m uppercase Latin letters — the book title. The strings are pairwise distinct.

Output

Output n integers — the indices of the strings after they are sorted asc-desc-endingly.

Example

Input


5 2
AA
AB
BB
BA
AZ


Output


5 2 1 3 4

Note

The following illustrates the first example.

<image>
import os
import sys
import math
from io import BytesIO, IOBase
from collections import deque,defaultdict,OrderedDict,Counter
from heapq import heappush,heappop,heapify
from bisect import bisect_right,insort,bisect_left
from functools import lru_cache
from itertools import permutations

sys.setrecursionlimit(10**6)

def STRIN():return input()
def INTIN():return int(input())
def LINT():return list(map(int,input().split()))
def LSTR():return list(map(str,input().split()))
def MINT():return map(int,input().split())
def MSTR():return map(str,input().split())



def solve():
   
   
    n,m=map(int,input().split())

    s=[]
    d={}
    ans=[]
    for i in range(n):
        s.append(input())



    s=''.join(s)
    s=list(s)
    for j in range(1,len(s),2):
        if (j+1)%2==0:
            s[j]=chr(90-(ord(s[j])+26-91))


    for i in range(0,len(s),m):
        ans.append(''.join(s[i:i+m]))

    for i in range(len(ans)):
        d[ans[i]]=i+1

    ans.sort()
    for i in ans:
        print(d[i],end=" ")

    



 
        
 
 
    

def main():
    #for _ in range(INTIN()):
    solve()
        





# region fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion

if __name__ == "__main__":
    main()

