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The protesters have set a seven-day deadline for Shahabuddin's removal and laid out a five-point demand.
Shakib is considered the greatest cricketer Bangladesh has ever produced but his political past places the former captain in a tricky position as an interim government supervises a power transition.
Samson's 111 helped India to their highest T20I score of 297/6.
Nitish Kumar Reddy hit 74 and bagged two wickets as India won by 86 runs.
The 25-year-old, who is leading the Indian pace attack in the ongoing T20I series against Bangladesh, made his debut just two years ago but has already played 55 T20Is, including two World Cups.
The 33-year-old, whose India career came to an abrupt halt after an underwhelming debut in the 2021 T20 World Cup, took three wickets against Bangladesh in the series opener on Sunday night.
Varun Chakravarthy and Arshdeep Singh starred as the visitors were bowled out for 127.
The outright victory consolidated India's pole position in the ICC World Test Championship Table (WTC) with 74.24 percentage points.
Bangladesh trail by 26 runs with eight wickets in hand at close on Day 4.
The 50-run mark was breached in a mere three overs against Bangladesh on the fourth day of the Kanpur Test.
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