THE QUESTION
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You are exploring a rectangular robot base arranged in an N × M grid. Each cell contains a tile that emits energy when stepped on. You start at cell S, and your goal is to reach cell T . Each step increases the energy cost, depending on the difference in energy intensity between the current cell and the next one. You must escape using as little energy as possible to avoid detection. Each cell contains: • ’0’ to ’9’ → energy intensity (0 = inert, 9 = strongest) • Walls ’#’ → blocked cells • S → Start cell • T → Target cell • ’.’ → empty cell with energy intensity 0 Movement Cost Calculation: If you move from cell ( x1, y1) with energy A to cell (x2, y2) with energy B: cost = 1 + |A − B|2 Examples: • From 3 → 3: cost = 1 + |3 − 3|2 = 1 • From 2 → 8: cost = 1 + |2 − 8|2 = 37 • From . → 7: cost = 1 + |0 − 7|2 = 50 (’.’ = energy 0) Input format: • First line: N M (1 ≤ N, M≤ 2000) • Next N lines: grid rows of M columns Output format: A single integer → minimum cost Sample Input: 5 7 1..3..2 ..#..#. S23..4T .#....# 9..8..7 Sample Output: 32 Input 40 80 30#.879.3390#.31844#.6##060..0038.15#97#0.7#.6#2#..#75#.#.89521234.64..#0#..88#. 77#.#9.57##1#1.#34#6#1.#36#.0##7#182870#91.507.#4516#.#.987#4979##06.4749#.3#033 8967#81.#9#81#8..7##.2#.#..39.##70.04.#8####.#27##8154#.#.287##62190##24#.5##716 428###33755#357#..8#1.#.##.9#20.9...#744..4.792##7#74749..53#095.73###9.4#533291 #3.2#.8.27####3#.8.4#4#.2#0#4##35#714182906837##438.#494.#35#283.##.#7#.###.5#.5 694##36103T289932825424612851409727#.#####2.0#.5#9...1#3#778971##8##.##7#169101# 02#7#85##566..9.710#.6#.###..#7##816#7.###25####5..#51482.##.54#7#3#75#.#610#### ##9#.4.438.#7##..1991##851#..#016##6935#2.5588#619#9#3#159#8#9##7.1937..#2.#69#4 .#.4.0304#6##3#42#.907#2#5.#959###85#8#541#22.9#1..4#.9.#9##3#8#0#725..0#02#425. 402##68..8##2##98#5##.#17#91.11#.#.745##2151#.#694##38#10#3#8#84##0131##.3##7#7# .884..35.9##1##1#0834.#7..#438#.###8#80937.62#3.2#.3#.#935#6.6#3460.55527#5#818# .0.98.9.4441#7###8#1.1602##1#8#6###.##9##4285810##294.10.6483.7#270100#0#.....2# 1427#320#6#4..3.#.####458#43#7##.##5.14..48#920#663.3#2.37#0#282.9196417.6###5.. 75.###89..3#5##..##8.9.#.199#0#2##1##2.#.1791.57..##.3220174.4#8###.9##.7######5 6#8793##7.91.2#######701.420###067.7#.#97#225.65178#92..#067268.8.3#2#1.##53.8## 516.5#86#9#9#..9#0#328#.76#1.##55.0.#8868#4#274#89.#.1#.##9.6#.9940#1.5##6.5#..3 319040159.3#.087196863.#3572##3###2.6#4.#.####95#.6.0##92.1#70284#8###537#29687# #597##.3##538#93####1.##1.04#78####.#6#####76448#.#1.#685..#2.#9.0#1##99.6##6154 .0#3#883.####094##7233#49##9#6##2...536#1##60#70###032#.#####..52#..####222###.3 1.1#2#07#.54.#68714..##392.#7.5#3.76#625#017.#17696#69##.516920#62#.06.2#0#.#4#2 ###8##5.#..#42.#1289#883#####2#502373##56#422#..83.#.###6936#5.5377#.292#760#9.# 4#.#.#1##.#6#05#53.#.5#.0##.#765#3.13#.#0###5###361##678.0##7.##.#3##20.6#14#... ####98###71#229.8#1..96###5##.29626#8#7444.##4###164#.#..36#8#0#28349##8.###2#84 968#2.##9#.#####7##62#..#4#145###1#7###8..9#.#.##.#39#8.#..92218#97#.#93.####### ##9##4#.23..2##.2#.7#8##573#24#..22####428..5392.914#.822#96#300#.4#88#851.#32.3 168.16.0#89#7#46#.#25###8#.5.7#1#74#7530##63#64#8##9.#71860.6..593.#0.#2.082#9## ##27#74#70#..732007##25582###0#.315.7##24#.077..#.#56####12###.3#.3.##7.3#.930.3 .#4..#8#8#92...###.546##6#4...#2#.##3.4.9#####.544#817#27#.#0.1###1#6#4#085##.03 4..#9#7##33.36#65##2.9#7..5#.#526#.#.3.##83#.9#7#6.3879##7...3#90#.506.7##68##.0 #030#5#58481#9349102#22#3465772##5#173#1516##66#601###95.###5#08.####958.#.9#08# 92#.979#0#7...#.67##085418.#36#.4#65.##209.656#8.#0.4124##3..6.8#006327#..6.#6## 9...#0.9.3#1498594615.#4.97#0#28###8..#9##3#8.1.#.6057981398054#2.##8.93#0..1#.# ##514.#.6722.927#.7#.7##4##9#####8#7..#.478#62.33420..#11#32.#..5.#.797164##..## #.##7#2#6.8##6#9928#3##37.3#414802.1#5722##644#10.0#9..#2.2292#4#4..541#..09##58 #41.##10#1..2#5##44#..2#7.0##8#.###8#8#..03##4.8#6.#.6#7#45616936630746.09.8.7.# #9.5#.8#38..##48#6#.01#7##4..4#821.#0#.6#5###36198#.9.#0##6...##.8#6#766###3.#7# #0#3#231396.#..7#.3#2.#2#.9#011918739##5#5..0#7.40##0.#98.##3#61#7#.#363..0#2#.5 22#1#98##..473181#213#8#.33#6....#50.#170603#5....##252369.12616##.4#082S86###82 83..711..7612#2.7529#2.#15.6#940#207.125##.1##.#8###37.1##9056#.89.679.883.##.0# 1##3.71.4#7526###..450###98#.5#6.51###8#6#2377###.#0##6710.###6#019#..858#.##1#7