A pair of acoustic engineers each recorded a resonance spectrum from the same instrument on different days. Each spectrum is written as a sequence of terms, where every term has an integer amplitude and a distinct non-negative integer frequency index, and the terms in each spectrum are listed in strictly decreasing order of frequency (no two terms in the same spectrum share a frequency).

The engineers want to fuse their two spectra into one combined reading: for every frequency that appears in either spectrum, the fused amplitude at that frequency is the sum of the amplitudes contributed by each original spectrum (treating a frequency missing from a spectrum as contributing amplitude 0). If a fused amplitude comes out to exactly 0, that frequency is omitted entirely from the fused spectrum — it did not survive the fusion.

Given both spectra, output the fused spectrum, listing its terms in strictly decreasing order of frequency.

Input format

Line 1: an integer n1, the number of terms in the first spectrum. Each of the next n1 lines: two integers amp freq — a term of the first spectrum. Frequencies strictly decrease from one line to the next. Next line: an integer n2, the number of terms in the second spectrum. Each of the next n2 lines: two integers amp freq — a term of the second spectrum, frequencies strictly decreasing.

Output format

Line 1: an integer k, the number of terms in the fused spectrum. Each of the next k lines: two integers amp freq, the fused spectrum's terms in strictly decreasing order of frequency. If k = 0, print only the line containing 0.

Constraints

• 0 <= n1, n2 <= 1000
• 0 <= freq <= 100000, and within each input spectrum all frequencies are distinct and strictly decreasing as listed
• Every input amplitude is a nonzero integer with -1000 <= amp <= 1000
• A fused amplitude, once computed, always fits in a 32-bit signed integer

3
5 4
2 2
9 0
3
3 4
-2 2
-9 0

1
8 4

2
1 5
2 1
2
4 3
1 0

4
1 5
4 3
2 1
1 0