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+"""Bisection algorithms."""
+
+def insort_right(a, x, lo=0, hi=None):
+ """Insert item x in list a, and keep it sorted assuming a is sorted.
+
+ If x is already in a, insert it to the right of the rightmost x.
+
+ Optional args lo (default 0) and hi (default len(a)) bound the
+ slice of a to be searched.
+ """
+
+ if lo < 0:
+ raise ValueError('lo must be non-negative')
+ if hi is None:
+ hi = len(a)
+ while lo < hi:
+ mid = (lo+hi)//2
+ if x < a[mid]: hi = mid
+ else: lo = mid+1
+ a.insert(lo, x)
+
+insort = insort_right # backward compatibility
+
+def bisect_right(a, x, lo=0, hi=None):
+ """Return the index where to insert item x in list a, assuming a is sorted.
+
+ The return value i is such that all e in a[:i] have e <= x, and all e in
+ a[i:] have e > x. So if x already appears in the list, a.insert(x) will
+ insert just after the rightmost x already there.
+
+ Optional args lo (default 0) and hi (default len(a)) bound the
+ slice of a to be searched.
+ """
+
+ if lo < 0:
+ raise ValueError('lo must be non-negative')
+ if hi is None:
+ hi = len(a)
+ while lo < hi:
+ mid = (lo+hi)//2
+ if x < a[mid]: hi = mid
+ else: lo = mid+1
+ return lo
+
+bisect = bisect_right # backward compatibility
+
+def insort_left(a, x, lo=0, hi=None):
+ """Insert item x in list a, and keep it sorted assuming a is sorted.
+
+ If x is already in a, insert it to the left of the leftmost x.
+
+ Optional args lo (default 0) and hi (default len(a)) bound the
+ slice of a to be searched.
+ """
+
+ if lo < 0:
+ raise ValueError('lo must be non-negative')
+ if hi is None:
+ hi = len(a)
+ while lo < hi:
+ mid = (lo+hi)//2
+ if a[mid] < x: lo = mid+1
+ else: hi = mid
+ a.insert(lo, x)
+
+
+def bisect_left(a, x, lo=0, hi=None):
+ """Return the index where to insert item x in list a, assuming a is sorted.
+
+ The return value i is such that all e in a[:i] have e < x, and all e in
+ a[i:] have e >= x. So if x already appears in the list, a.insert(x) will
+ insert just before the leftmost x already there.
+
+ Optional args lo (default 0) and hi (default len(a)) bound the
+ slice of a to be searched.
+ """
+
+ if lo < 0:
+ raise ValueError('lo must be non-negative')
+ if hi is None:
+ hi = len(a)
+ while lo < hi:
+ mid = (lo+hi)//2
+ if a[mid] < x: lo = mid+1
+ else: hi = mid
+ return lo
+
+# Overwrite above definitions with a fast C implementation
+try:
+ from _bisect import *
+except ImportError:
+ pass