Microwave Keypad Effort

Medium

A microwave timer is set by typing one to four digits. The digits are padded with zeros on the left to four: the first two are minutes, the last two are seconds, and the cooking time is minutes × 60 + seconds. Both minutes and seconds may be anything from 00 to 99, so typing 1 9 0 means 1 minute 90 seconds, i.e. 150 seconds. Your finger starts above digit start_digit. Moving the finger to a different digit costs move_cost, and pressing the digit under the finger costs press_cost. Return the minimum effort needed to set exactly seconds seconds.

Example 1

start_digit=5, move_cost=3, press_cost=1, seconds=90 → 8

Typing 1 3 0 (1 min 30 s) costs 3+1 + 3+1 + 3+1 = 12, while 9 0 (0 min 90 s) costs 3+1 + 3+1 = 8. The answer is 8.

Example 2

start_digit=4, move_cost=10, press_cost=2, seconds=44 → 4

The finger is already on 4: press it twice without moving. 2 + 2 = 4.

Example 3

start_digit=0, move_cost=1, press_cost=5, seconds=6039 → 21

Constraints

0 ≤ start_digit ≤ 9
1 ≤ move_cost, press_cost ≤ 10⁵
1 ≤ seconds ≤ 6039

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Topics

Math Enumeration

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Input

start_digit=5, move_cost=3, press_cost=1, seconds=90

Expected

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