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A. Shaass and Oskols

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputShaass has decided to hunt some birds. There are *n* horizontal electricity wires aligned parallel to each other. Wires are numbered 1 to *n* from top to bottom. On each wire there are some oskols sitting next to each other. Oskol is the name of a delicious kind of birds in Shaass's territory. Supposed there are *a*_{i} oskols sitting on the *i*-th wire.

Sometimes Shaass shots one of the birds and the bird dies (suppose that this bird sat at the *i*-th wire). Consequently all the birds on the *i*-th wire to the left of the dead bird get scared and jump up on the wire number *i* - 1, if there exists no upper wire they fly away. Also all the birds to the right of the dead bird jump down on wire number *i* + 1, if there exists no such wire they fly away.

Shaass has shot *m* birds. You're given the initial number of birds on each wire, tell him how many birds are sitting on each wire after the shots.

Input

The first line of the input contains an integer *n*, (1 ≤ *n* ≤ 100). The next line contains a list of space-separated integers *a*_{1}, *a*_{2}, ..., *a*_{n}, (0 ≤ *a*_{i} ≤ 100).

The third line contains an integer *m*, (0 ≤ *m* ≤ 100). Each of the next *m* lines contains two integers *x*_{i} and *y*_{i}. The integers mean that for the *i*-th time Shaass shoot the *y*_{i}-th (from left) bird on the *x*_{i}-th wire, (1 ≤ *x*_{i} ≤ *n*, 1 ≤ *y*_{i}). It's guaranteed there will be at least *y*_{i} birds on the *x*_{i}-th wire at that moment.

Output

On the *i*-th line of the output print the number of birds on the *i*-th wire.

Examples

Input

5

10 10 10 10 10

5

2 5

3 13

2 12

1 13

4 6

Output

0

12

5

0

16

Input

3

2 4 1

1

2 2

Output

3

0

3

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