"""Bisection algorithms."""

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def insort_right(a, x, lo=0, hi=None):

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"""Insert item x in list a, and keep it sorted assuming a is sorted.

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If x is already in a, insert it to the right of the rightmost x.

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Optional args lo (default 0) and hi (default len(a)) bound the

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slice of a to be searched.

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"""

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lo = bisect_right(a, x, lo, hi)

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a.insert(lo, x)

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def bisect_right(a, x, lo=0, hi=None):

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"""Return the index where to insert item x in list a, assuming a is sorted.

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The return value i is such that all e in a[:i] have e <= x, and all e in

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a[i:] have e > x. So if x already appears in the list, a.insert(x) will

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insert just after the rightmost x already there.

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Optional args lo (default 0) and hi (default len(a)) bound the

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slice of a to be searched.

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"""

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if lo < 0:

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raise ValueError('lo must be non-negative')

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if hi is None:

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hi = len(a)

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while lo < hi:

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mid = (lo+hi)//2

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# Use __lt__ to match the logic in list.sort() and in heapq

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if x < a[mid]: hi = mid

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else: lo = mid+1

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return lo

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def insort_left(a, x, lo=0, hi=None):

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"""Insert item x in list a, and keep it sorted assuming a is sorted.

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If x is already in a, insert it to the left of the leftmost x.

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Optional args lo (default 0) and hi (default len(a)) bound the

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slice of a to be searched.

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"""

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lo = bisect_left(a, x, lo, hi)

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a.insert(lo, x)

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def bisect_left(a, x, lo=0, hi=None):

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"""Return the index where to insert item x in list a, assuming a is sorted.

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The return value i is such that all e in a[:i] have e < x, and all e in

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a[i:] have e >= x. So if x already appears in the list, a.insert(x) will

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insert just before the leftmost x already there.

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Optional args lo (default 0) and hi (default len(a)) bound the

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slice of a to be searched.

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"""

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if lo < 0:

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raise ValueError('lo must be non-negative')

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if hi is None:

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hi = len(a)

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while lo < hi:

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mid = (lo+hi)//2

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# Use __lt__ to match the logic in list.sort() and in heapq

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if a[mid] < x: lo = mid+1

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else: hi = mid

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return lo

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# Overwrite above definitions with a fast C implementation

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try:

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from _bisect import *

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except ImportError:

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pass

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# Create aliases

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bisect = bisect_right

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insort = insort_right

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