# Partition to pairs

Space archaeologists discovered on the planet in the neighbouring star system n ancient artefacts, which they numbered from 1 to n. Each artefact has k different parameters, each parameter is characterised by an integer. The artefact i has the parameters `a[i,1]`

, `a[i,2]`

, ... `a[i,k]`

. It turned out that the first parameters for all artefacts are different: for all i ≠ j, `a[i,1]`

≠ `a[j,1]`

is satisfied, while other parameters for the artefacts may coincide.

Scientists also discovered a text according to which, in order to activate artefacts, they must be specially paired and combined. The partition of artefacts is correct if for each t from 1 to k you can choose such a number `b[t]`

that it lies on the interval between the values of t-th parameter of artefacts of each pair. That is, artefacts i and j form a pair, if holds the condition `a[i,t]`

≤ `b[t]`

≤ `a[j,t]`

or the condition `a[i,t]`

≥ `b[t]`

≥ `a[j,t]`

.

Now scientists want to find out if the text is correctly decrypted. To do this, you need to check whether there is a correct splitting of artefacts into pairs. Each artefact must enter exactly one pair in the split.

Write a program that, according to the description of the parameters of the artefacts, determines whether it is possible to split them into pairs so that for each parameter there is a value lying between the values of this parameter of the artefacts of each pair, and in the case of a positive answer displays such partition.

## Input

First line contains integers n and k (2 ≤ n ≤ 2 * `10^5`

, n is even, 1 ≤ k ≤ 7) - number of artefacts and number of parameters. Each of the next n lines contains k integers `a[i,1]`

, `a[i,2]`

, ..., `a[i,k]`

- the parameters of artefacts (`-10^9`

≤ `a[i,j]`

≤ `10^9`

, all values of `a[i,1]`

are different).

## Output

Print "NO" if the required pairing does not exist.

Otherwise, print "YES" in the first line. Then print n / 2 lines, in each line print two numbers - the numbers of artefacts that make a pair. Each artefact must be displayed exactly once.

If there are several valid pairs of artefacts, output any of them.