Problem: Mr. Kitayuta has kindly given you a string s consisting of lowercase English letters. You are asked to insert exactly one lowercase English letter into s to make it a palindrome. A palindrome is a string that reads the same forward and backward. For example, "noon", "testset" and "a" are all palindromes, while "test" and "kitayuta" are not.

You can choose any lowercase English letter, and insert it to any position of s, possibly to the beginning or the end of s. You have to insert a letter even if the given string is already a palindrome.

If it is possible to insert one lowercase English letter into s so that the resulting string will be a palindrome, print the string after the insertion. Otherwise, print "NA" (without quotes, case-sensitive). In case there is more than one palindrome that can be obtained, you are allowed to print any of them.

Input

The only line of the input contains a string s (1 ≤ |s| ≤ 10). Each character in s is a lowercase English letter.

Output

If it is possible to turn s into a palindrome by inserting one lowercase English letter, print the resulting string in a single line. Otherwise, print "NA" (without quotes, case-sensitive). In case there is more than one solution, any of them will be accepted. 

Examples

Input

revive


Output

reviver


Input

ee


Output

eye

Input

kitayuta


Output

NA

Note

For the first sample, insert 'r' to the end of "revive" to obtain a palindrome "reviver".

For the second sample, there is more than one solution. For example, "eve" will also be accepted.

For the third sample, it is not possible to turn "kitayuta" into a palindrome by just inserting one letter.

Solution (in PYTHON):

Solution:
import sys
from operator import itemgetter

from operator import mul    # or mul=lambda x,y:x*y
from fractions import Fraction


def palypalo(pal, inserted, fucked_up):

    n_pal = len(pal)
    # print 
    # print pal, n_pal
    for i_pal in range(n_pal):
        # print 
        # print i_pal,
        if pal[i_pal] != pal[n_pal - 1 - i_pal]:
            # print 
            # print pal[i_pal], pal[n_pal - 1 - i_pal]
            if inserted:
                fucked_up = True
                return "NA"


            if pal[i_pal] == pal[n_pal - 2 - i_pal] and pal[i_pal] == pal[n_pal - 2 - i_pal]:
                pal1 = palypalo(pal[:i_pal] + pal[n_pal - 1 - i_pal] + pal[i_pal:], True, fucked_up)
                pal2 = palypalo(pal[:n_pal - i_pal] + pal[i_pal] + pal[n_pal - i_pal:], True, fucked_up)
                # print "pal1:", pal1
                # print "pal2:", pal2
                if pal1 != "NA":
                    pal = pal1
                else:
                    pal = pal2
                return pal     

            elif pal[i_pal] == pal[n_pal - 2 - i_pal]:
                pal = pal[:i_pal] + pal[n_pal - 1 - i_pal] + pal[i_pal:]
            elif pal[i_pal + 1] == pal[n_pal - 1 - i_pal]:
                pal = pal[:n_pal - i_pal] + pal[i_pal] + pal[n_pal - i_pal:]

            else:
                fucked_up = True
                return "NA"
            # print pal 
            # print 

            inserted = True
            n_pal += 1 
    if fucked_up:
        return "NA"
    else:
        if not(inserted):
            # if n_pal % 2 == 0:
            #     pal = pal[:int(n_pal/2)]+'a'+pal[int(n_pal/2):]
            # else :
            pal = pal[:int(n_pal/2)]+pal[int(n_pal/2)]+pal[int(n_pal/2):]
        return pal

def main():
    pal = sys.stdin.readline().strip()
    inserted = False
    fucked_up = False


    pal = palypalo(pal, False, False)

    print pal 


main()