Count the Overlap

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Problem

Each line of input will be the position and size of three rectagles (a, b and c). The task is to count how much each pairing and all three of the rectangles overlap.

Example input:

ax 1 ay 1 aw 5 ah 5 bx 3 by 3 bw 7 bh 5 cx 5 cy 4 cw 7 ch 3

x,y indicates each rectangle's top left corner. w,h it's width and height. So visually ax 1 ay 1 aw 5 ah 5 would be:

aaaaa........
aaaaa........
aaaaa........
aaaaa........
aaaaa........
.............
.............
.............

Adding b(bx 3 by 3 bw 7 bh 5):

aaaaa........
aaaaa........
aa111bbbb....
aa111bbbb....
aa111bbbb....
..bbbbbbb....
..bbbbbbb....
.............

the 1s indicate on how many squares a and b overlap. It's the same with the c rectagle.
Asked output:

ab 9 ac 2 bc 15 abc 2

Options

exec is denied

now post-mortem time, all source codes will be revealed

Sample input:_

ax 1 ay 1 aw 1 ah 1 bx 1 by 1 bw 1 bh 1 cx 1 cy 1 cw 1 ch 1

Sample output:

ab 1 ac 1 bc 1 abc 1

Sample input:_

ax 3 ay 4 aw 4 ah 11 bx 1 by 3 bw 3 bh 4 cx 5 cy 2 cw 6 ch 3
ax 2 ay 4 aw 7 ah 10 bx 4 by 1 bw 11 bh 5 cx 3 cy 2 cw 8 ch 5
ax 4 ay 2 aw 5 ah 5 bx 5 by 1 bw 11 bh 10 cx 2 cy 2 cw 6 ch 11
ax 2 ay 4 aw 4 ah 6 bx 1 by 1 bw 11 bh 8 cx 1 cy 4 cw 4 ch 3
ax 1 ay 1 aw 4 ah 4 bx 2 by 4 bw 7 bh 5 cx 1 cy 2 cw 7 ch 8

Sample output:

ab 3 ac 2 bc 0 abc 0
ab 10 ac 18 bc 28 abc 10
ab 20 ac 20 bc 27 abc 15
ab 20 ac 9 bc 12 abc 9
ab 3 ac 12 bc 30 abc 3

Sample input:_

ax 17 ay 20 aw 34 ah 15 bx 13 by 11 bw 19 bh 24 cx 10 cy 19 cw 19 ch 28
ax 18 ay 22 aw 7 ah 8 bx 19 by 19 bw 29 bh 12 cx 15 cy 14 cw 30 ch 19
ax 16 ay 8 aw 29 ah 12 bx 13 by 21 bw 28 bh 28 cx 22 cy 14 cw 5 ch 11
ax 13 ay 9 aw 34 ah 30 bx 21 by 8 bw 12 bh 12 cx 17 cy 8 cw 16 ch 28
ax 8 ay 12 aw 5 ah 27 bx 8 by 6 bw 29 bh 1 cx 10 cy 5 cw 4 ch 25
ax 22 ay 14 aw 26 ah 6 bx 22 by 17 bw 10 bh 3 cx 17 cy 16 cw 20 ch 6
ax 14 ay 17 aw 29 ah 16 bx 15 by 13 bw 19 bh 16 cx 23 cy 10 cw 35 ch 1
ax 9 ay 5 aw 7 ah 23 bx 9 by 6 bw 6 bh 34 cx 14 cy 16 cw 2 ch 22
ax 23 ay 1 aw 5 ah 22 bx 20 by 12 bw 7 bh 19 cx 18 cy 22 cw 37 ch 35
ax 20 ay 5 aw 7 ah 11 bx 18 by 4 bw 35 bh 12 cx 13 cy 15 cw 1 ch 26
ax 14 ay 18 aw 18 ah 30 bx 22 by 3 bw 9 bh 4 cx 10 cy 19 cw 11 ch 13
ax 19 ay 22 aw 36 ah 33 bx 21 by 13 bw 34 bh 17 cx 10 cy 14 cw 18 ch 17
ax 22 ay 13 aw 22 ah 19 bx 17 by 12 bw 19 bh 31 cx 17 cy 8 cw 13 ch 25
ax 16 ay 17 aw 33 ah 35 bx 8 by 14 bw 6 bh 19 cx 9 cy 22 cw 8 ch 16
ax 19 ay 7 aw 7 ah 5 bx 12 by 2 bw 25 bh 10 cx 8 cy 23 cw 5 ch 1
ax 16 ay 18 aw 5 ah 29 bx 19 by 1 bw 31 bh 20 cx 15 cy 8 cw 36 ch 19
ax 17 ay 12 aw 31 ah 33 bx 20 by 8 bw 21 bh 16 cx 19 cy 12 cw 10 ch 31
ax 20 ay 20 aw 15 ah 6 bx 22 by 4 bw 23 bh 3 cx 8 cy 5 cw 25 ch 15
ax 14 ay 8 aw 29 ah 5 bx 23 by 13 bw 28 bh 12 cx 16 cy 22 cw 10 ch 36
ax 16 ay 22 aw 37 ah 14 bx 16 by 19 bw 16 bh 3 cx 15 cy 2 cw 20 ch 29
ax 22 ay 6 aw 32 ah 15 bx 22 by 13 bw 8 bh 28 cx 19 cy 3 cw 31 ch 29
ax 10 ay 23 aw 26 ah 5 bx 22 by 18 bw 6 bh 32 cx 11 cy 10 cw 25 ch 32
ax 19 ay 8 aw 26 ah 1 bx 22 by 18 bw 8 bh 35 cx 21 cy 19 cw 16 ch 19
ax 9 ay 11 aw 4 ah 1 bx 14 by 16 bw 16 bh 17 cx 12 cy 3 cw 24 ch 29
ax 15 ay 6 aw 36 ah 15 bx 19 by 8 bw 5 bh 25 cx 10 cy 13 cw 32 ch 20

Sample output:

ab 225 ac 180 bc 256 abc 180
ab 48 ac 56 bc 312 abc 48
ab 0 ac 30 bc 20 abc 0
ab 132 ac 432 bc 144 abc 132
ab 0 ac 54 bc 4 abc 0
ab 30 ac 60 bc 30 abc 30
ab 228 ac 0 bc 0 abc 0
ab 132 ac 24 bc 22 abc 12
ab 44 ac 5 bc 63 abc 4
ab 77 ac 0 bc 0 abc 0
ab 0 ac 91 bc 0 abc 0
ab 272 ac 81 bc 112 abc 56
ab 266 ac 152 bc 273 abc 152
ab 0 ac 16 bc 55 abc 0
ab 35 ac 0 bc 0 abc 0
ab 6 ac 45 bc 403 abc 6
ab 252 ac 310 bc 108 abc 108
ab 0 ac 0 bc 22 abc 0
ab 0 ac 0 bc 9 abc 0
ab 0 ac 171 bc 48 abc 0
ab 64 ac 420 bc 152 abc 64
ab 30 ac 125 bc 144 abc 30
ab 0 ac 0 bc 152 abc 0
ab 0 ac 1 bc 256 abc 0
ab 65 ac 216 bc 100 abc 40

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