Black and White Components

Draw a bounded grid with the requested black and white component counts at low weighted area.

Solution Interface

Submit a zip_project solution. The run command is executed once per case, reads the case from standard input, and writes the answer to standard output. The trusted separated evaluator runs the migrated Frontier-CS Testlib checker against the submitted output and the case's evaluator-only answer or scoring metadata.

Scoring

The leaderboard score is the average checker ratio scaled to 0..100 across official cases. Invalid outputs receive zero for the affected case. The public validation case is intentionally tiny and deterministic; official scoring uses the source-derived Frontier-CS cases packaged as private benchmark data.

Original Statement

Black and White

Time limit: 2 seconds Memory limit: 256 megabytes

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The jury has a great artistic idea — to create a rectangular panel out of a huge pile of black and white squares of the same size. The panel should have exactly b 4-connected areas made of black tiles, and w 4-connected areas made of white tiles.

A 4-connected area of some color is a maximal set of the panel tiles such that: • any two tiles of the area share the same color; • for any two tiles of the area there is a tile sequence connecting them, such that any two consecutive tiles of the sequence share a common side.

You will also be given two integers x, y. Try to minimize x * (the number of black tiles in your grid) + y * (the number of white tiles in your grid).

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Input

The only line of the input file contains four integers b, w — number of black and white areas (1 ≤ b, w ≤ 1000) and x, y - grading coefficients (1 ≤ x, y ≤ 1000).

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Output

The first line of the output file should contain the picture sizes r and c — the number of rows and columns (1 ≤ r, c ≤ 100 000). This line should be followed by r lines of c symbols each. Each symbol should be either '@' (for black tile) or '.' (for white one). There should be no more than 100 000 tiles in the panel.

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Example

Input: 2 3 5 6

Output: 6 7 @@@@@@@ @.@@@@@ @@...@@ @@@@@@@ ....... @@@@@@@