- 126

## Statement

## Goal

Hamming Codes are a way of validating and fixing blocks of binary data using**parity bits**. Each block is

**2^**bits long. Here, we are only interested in the case where

`N``N = 4`(i.e.

**16**bit blocks)

Consider the following, generic, block of data,

a b c d

e f g h

i j k l

m n o p

- Bit

**a**is a global parity bit. A valid message has an

**even**number of

**1**'s

- Bit

**b**is a parity bit for the bits

**[d, f, h, j, l, n, p]**(

**odd**columns), meaning that the subset

**even**number of

**1**'s.

- Bit

**c**is a parity check on bits

**[d, g, h, k, l, o, p]**(

**last two**columns), meaning that the subset

**even**number of

**1**'s.

- Bit

**e**is a parity check on bits

**[f, g, h, m, n, o, p]**(

**odd**lines), meaning that the subset

**even**number of

**1**'s.

- Bit

**i**is a parity check on bits

**[j, k, l, m, n, o, p]**(

**last two**lines), meaning that the subset

**even**number of

**1**'s.

Given a message encoded with this error-checking algorithm, it's possible to locate any 1 faulty bit and correct it, and locate if there are 2 faulty bits (but not correct them).

For instance, if

**odd**,

**even**,

**even**and

**odd**, then the bit

**j**needs to be flipped. Furthermore, bit

**a**can be used to detect if there are 2 errors in the block. If bit

**j**needs to be flipped, but the whole message is

**even**, then there are two errors.

You are given a string in binary of length 16. Your goal is to check whether this string has an error, and if so correct it. If the string has only one error, or is valid, print out the corrected string. Print out 'TWO ERRORS' if the string has two errors.

Input

**Line 1:**A string of 16 binary digits, representing a message block protected with the Hamming ECC scheme.

Output

If the message has

If it has

If it has

**no errors**: print out the**original**message.If it has

**1 error**: print out the**corrected**message.If it has

**2 errors**: print out**'TWO ERRORS'**.Constraints

At most 2 errors in the message.

Example

Input

1100101010110110

Output

1100101011110110

A higher resolution is required to access the IDE