## Reorder Terms

Statement

## Goal

You are given**n**rows with three terms per line separated by a space.

...

Reorder these rows from lowest value to highest value. Calculate the value of these rows using Value = a*b + c. The test cases will be written such that there are no ties.

Example:

3 2 1

1 1 1

-1 0 5

3 2 1 = 3*2 + 1 =7

1 1 1 = 1*1 + 1 = 2

-1 0 5 = -1*0 +5 = 5

Result:

1 1 1

-1 0 5

3 2 1

Input

**n**number of rows

Output

Reordered rows

Constraints

1 < n <= 6

-128 <= a,b,c < 128

-128 <= a,b,c < 128

Example

Input

3 3 2 1 1 1 1 -1 0 5

Output

1 1 1 -1 0 5 3 2 1

Game modes

Fastest, Shortest

Test cases

Test 1 Test

Input

3
3 2 1
1 1 1
-1 0 5

Output

1 1 1
-1 0 5
3 2 1

Validator 1 Validator

Input

3
5 6 1
1 1 1
-2 0 3

Output

1 1 1
-2 0 3
5 6 1

Test 2 Test

Input

4
-1 -2 3
-2 5 1
3 -6 18
4 4 100

Output

-2 5 1
3 -6 18
-1 -2 3
4 4 100

Validator 2 Validator

Input

4
-1 -3 5
-2 6 1
-4 5 20
6 6 16

Output

-2 6 1
-4 5 20
-1 -3 5
6 6 16

Test 3 Test

Input

6
100 -1 -5
-1 0 1
0 0 3
2 4 6
0 5 2
-1 -1 -1

Output

100 -1 -5
-1 -1 -1
-1 0 1
0 5 2
0 0 3
2 4 6

Validator 3 Validator

Input

6
90 -1 -4
-2 0 2
0 0 5
3 4 8
0 5 3
-1 -1 -1

Output

90 -1 -4
-1 -1 -1
-2 0 2
0 5 3
0 0 5
3 4 8

Test 4 Test

Input

3
-128 -128 2
-128 127 0
0 0 127

Output

-128 127 0
0 0 127
-128 -128 2

Validator 4 Validator

Input

3
127 127 -2
-128 127 -128
0 1 127

Output

-128 127 -128
0 1 127
127 127 -2

Test 5 Test

Input

4
0 0 1
0 0 3
0 0 2
0 0 4

Output

0 0 1
0 0 2
0 0 3
0 0 4

Validator 5 Validator

Input

4
0 1 11
0 1 13
0 1 12
0 1 14

Output

0 1 11
0 1 12
0 1 13
0 1 14

Solution language

Solution

Stub generator input

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