PageThere is a famous railway station in PopPush City. Country there is incredibly hilly. The station wasbuilt in last century. Unfortunately, funds wwere extremely limited that time. It was possible toestablish only a surface track. Moreover, it turned out that the station could be only a dead-endone (see picture) and due to lack of available space it could have only one track.5, 4, 3, 2, 11, 2, 3, 4, 5StationThe local tradition is that every train arriving from the direction A continues in the direction B withcoaches reorganized in some way.• Assume that the train arriving from the direction A has NS 1000 coaches numbered inincreasing order 1, 2, . N.• The chieffor train reorganizations must know whether it is possible to marshal coachescontinuing in the direction B so that their order will be a, a2. . aN. Help him and write aprogram that decides whether it is possible to get the required order of coaches.• You can assume that single coaches can be disconnected from the train before they enterthe station and that they can move themselves until they are on the track in the direction B.• You can also suppose that at any time there can be located as many coaches as necessary inthe station. But once a coach has entered the station it cannot return to the track in thedirection A and also once it has left the station in the direction B it cannot return back to thestation.Program Input• The input file consists of blocks of lines, each of which is a test case. Each block except thelast describes one train and possibly more requirements for its reorganization. In the firstline of the block there is the integer N, which is the number of coaches in the train. In eachof the next lines of the block there is a permutation of 1, 2, . N. For example, if N is 5, andthe permutation could be 5, 3, 2. 1, 4. Your program will take this permutation as input anddetermine whether you can marshal the coaches from track A an incoming order 1, 2, 3, 4, 5to track B with an outgoing order 5, 3. 2, 1, 4 using the station, which can be treated as astack• The last line of the block contains just 0.If a block starts with a zero, the program will terminate.• You should use the input file named lablin.txt (download from Canvas) to test yourprogram; an output file named lab1out.txt (with correct output) is also provided for you toverify your program.Input Sample... Input Sample// start of first block1 2 3 455 4123// end of first block// start of second block654321// end of second block// end of inputProgram OutputThe output file contains the lines corresponding to the lines with permutations in the input file. Aline of the output file contains "Yes" if it is possible to marshal the coaches in the order requiredon the corresponding line of the input file. Otherwise it'contains "No". In addition. there is oneempty line after the lines corresponding to one block of the input file. There is no line in theoutput file corresponding to the last "nul" block of the input file.Output SampleThis is an output sample of the previous input sampleYesNOYesHintKey points to understand/solve the problem:• The train station can be regarded as a stack.• One can push a coach from track A into the stack when the coach is popped out of the stack,it gets into track B, and a coach in the station can never go back to track A.• Taking a train with 5 coaches as an exxample.• Coaches in track A is always in strictly increasing order, Le. 1. 2. 3, 4, 5The train chief tries to marshal the coaches into track B via a sequence of push and popoperations.• Each test case in the input file is asking a question: is it possible to marshal the the coachesinto track B such that the coach order matches the test case?o For instance, if the test case is "1, 2, 3, 4, 5", then we can perform the followingsequence of operations

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PageThere is a famous railway station in PopPush City. Country there is incredibly hilly. The station wasbuilt in last century. Unfortunately, funds wwere extremely limited that time. It was possible toestablish only a surface track. Moreover, it turned out that the station could be only a dead-endone (see picture) and due to lack of available space it could have only one track.5, 4, 3, 2, 11, 2, 3, 4, 5StationThe local tradition is that every train arriving from the direction A continues in the direction B withcoaches reorganized in some way.• Assume that the train arriving from the direction A has NS 1000 coaches numbered inincreasing order 1, 2, . N.• The chieffor train reorganizations must know whether it is possible to marshal coachescontinuing in the direction B so that their order will be a, a2. . aN. Help him and write aprogram that decides whether it is possible to get the required order of coaches.• You can assume that single coaches can be disconnected from the train before they enterthe station and that they can move themselves until they are on the track in the direction B.• You can also suppose that at any time there can be located as many coaches as necessary inthe station. But once a coach has entered the station it cannot return to the track in thedirection A and also once it has left the station in the direction B it cannot return back to thestation.Program Input• The input file consists of blocks of lines, each of which is a test case. Each block except thelast describes one train and possibly more requirements for its reorganization. In the firstline of the block there is the integer N, which is the number of coaches in the train. In eachof the next lines of the block there is a permutation of 1, 2, . N. For example, if N is 5, andthe permutation could be 5, 3, 2. 1, 4. Your program will take this permutation as input anddetermine whether you can marshal the coaches from track A an incoming order 1, 2, 3, 4, 5to track B with an outgoing order 5, 3. 2, 1, 4 using the station, which can be treated as astack• The last line of the block contains just 0.If a block starts with a zero, the program will terminate.• You should use the input file named lablin.txt (download from Canvas) to test yourprogram; an output file named lab1out.txt (with correct output) is also provided for you toverify your program.Input Sample... Input Sample// start of first block1 2 3 455 4123// end of first block// start of second block654321// end of second block// end of inputProgram OutputThe output file contains the lines corresponding to the lines with permutations in the input file. Aline of the output file contains &#34;Yes&#34; if it is possible to marshal the coaches in the order requiredon the corresponding line of the input file. Otherwise it'contains &#34;No&#34;. In addition. there is oneempty line after the lines corresponding to one block of the input file. There is no line in theoutput file corresponding to the last &#34;nul&#34; block of the input file.Output SampleThis is an output sample of the previous input sampleYesNOYesHintKey points to understand/solve the problem:• The train station can be regarded as a stack.• One can push a coach from track A into the stack when the coach is popped out of the stack,it gets into track B, and a coach in the station can never go back to track A.• Taking a train with 5 coaches as an exxample.• Coaches in track A is always in strictly increasing order, Le. 1. 2. 3, 4, 5The train chief tries to marshal the coaches into track B via a sequence of push and popoperations.• Each test case in the input file is asking a question: is it possible to marshal the the coachesinto track B such that the coach order matches the test case?o For instance, if the test case is &#34;1, 2, 3, 4, 5&#34;, then we can perform the followingsequence of operations

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