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Afridi's appointment comes in the build-up to New Zealand's two-Test tour of Pakistan, beginning on Monday.
After taking charge in 2016 Williamson captained New Zealand in 40 Tests - with 22 wins, 10 defeats and eight draws.
'Comparison is not a part of my life, I'm just 24-25 so you can compare once I'm 30-32. There's no logic in comparing before that,' Pant told Bhogle ahead of the third and final against New Zealand.
Having raced to 104/1 in 18 overs, helped by Finn Allen's breezy 57, New Zealand had looked on course for a 2-0 series victory until rain stopped play.
The home side chased down the 307-run target with 17 balls to spare, reaching 309 for 3 in 47.1 overs.
For New Zealand skipper Kane Williamson, the immediate target was to win the series against India.
Chasing New Zealand's 160, skipper Hardik Pandya hit an unbeaten 18-ball 30 as India were 75 for four in 9 overs when rain stopped play.
Surya smashed an unbeaten 111 off only 51 balls. He hit 11 fours and seven sixes.
Incessant rain made the ground unplayable at Wellington.
The beaten semifinalists of the recent T20 World Cup in Australia will clash in Wellington on Friday in the first T20 International of the three-match series.
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