|2017-2018 ACM-ICPC, NEERC, Southern Subregional Contest, qualification stage (Online Mirror, ACM-ICPC Rules, Teams Preferred)|
The Berland's capital has the form of a rectangle with sizes n × m quarters. All quarters are divided into three types:
A quarter labeled with letter 'A' produces q units of noise. A quarter labeled with letter 'B' produces 2·q units of noise. And so on, up to a quarter labeled with letter 'Z', which produces 26·q units of noise. There can be any number of quarters labeled with each letter in the city.
When propagating from the source of the noise, the noise level is halved when moving from one quarter to a quarter that shares a side with it (when an odd number is to be halved, it's rounded down). The noise spreads along the chain. For example, if some quarter is located at a distance 2 from the noise source, then the value of noise which will reach the quarter is divided by 4. So the noise level that comes from the source to the quarter is determined solely by the length of the shortest path between them. Heavily built-up quarters are obstacles, the noise does not penetrate into them.
The noise level in quarter is defined as the sum of the noise from all sources. To assess the quality of life of the population of the capital of Berland, it is required to find the number of quarters whose noise level exceeds the allowed level p.
The first line contains four integers n, m, q and p (1 ≤ n, m ≤ 250, 1 ≤ q, p ≤ 106) — the sizes of Berland's capital, the number of noise units that a quarter 'A' produces, and the allowable noise level.
Each of the following n lines contains m characters — the description of the capital quarters, in the format that was described in the statement above. It is possible that in the Berland's capital there are no quarters of any type.
Print the number of quarters, in which the noise level exceeds the allowed level p.
3 3 100 140
3 3 2 8
3 4 5 4
The illustration to the first example is in the main part of the statement.