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Bangladesh was bowled out for 168 in their second innings after resuming the day on 126-6.
Fast bowler Naseem Shah, who at 16 years, 359 days became the youngest-ever bowler to take a Test hat-trick on Sunday, finished with 4-26.
The second Test will be played after a two-month break, in Karachi from April 5 to 9. Brief scores: Bangladesh 233 and 168; Pakistan 445.