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187 lines
6.7 KiB
187 lines
6.7 KiB
/* SPDX-License-Identifier: GPL-2.0-or-later */ |
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/* |
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Interval Trees |
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(C) 2012 Michel Lespinasse <[email protected]> |
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include/linux/interval_tree_generic.h |
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*/ |
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#include <linux/rbtree_augmented.h> |
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/* |
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* Template for implementing interval trees |
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* |
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* ITSTRUCT: struct type of the interval tree nodes |
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* ITRB: name of struct rb_node field within ITSTRUCT |
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* ITTYPE: type of the interval endpoints |
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* ITSUBTREE: name of ITTYPE field within ITSTRUCT holding last-in-subtree |
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* ITSTART(n): start endpoint of ITSTRUCT node n |
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* ITLAST(n): last endpoint of ITSTRUCT node n |
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* ITSTATIC: 'static' or empty |
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* ITPREFIX: prefix to use for the inline tree definitions |
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* |
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* Note - before using this, please consider if generic version |
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* (interval_tree.h) would work for you... |
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*/ |
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#define INTERVAL_TREE_DEFINE(ITSTRUCT, ITRB, ITTYPE, ITSUBTREE, \ |
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ITSTART, ITLAST, ITSTATIC, ITPREFIX) \ |
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\ |
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/* Callbacks for augmented rbtree insert and remove */ \ |
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\ |
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RB_DECLARE_CALLBACKS_MAX(static, ITPREFIX ## _augment, \ |
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ITSTRUCT, ITRB, ITTYPE, ITSUBTREE, ITLAST) \ |
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\ |
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/* Insert / remove interval nodes from the tree */ \ |
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\ |
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ITSTATIC void ITPREFIX ## _insert(ITSTRUCT *node, \ |
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struct rb_root_cached *root) \ |
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{ \ |
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struct rb_node **link = &root->rb_root.rb_node, *rb_parent = NULL; \ |
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ITTYPE start = ITSTART(node), last = ITLAST(node); \ |
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ITSTRUCT *parent; \ |
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bool leftmost = true; \ |
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\ |
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while (*link) { \ |
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rb_parent = *link; \ |
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parent = rb_entry(rb_parent, ITSTRUCT, ITRB); \ |
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if (parent->ITSUBTREE < last) \ |
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parent->ITSUBTREE = last; \ |
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if (start < ITSTART(parent)) \ |
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link = &parent->ITRB.rb_left; \ |
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else { \ |
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link = &parent->ITRB.rb_right; \ |
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leftmost = false; \ |
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} \ |
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} \ |
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\ |
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node->ITSUBTREE = last; \ |
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rb_link_node(&node->ITRB, rb_parent, link); \ |
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rb_insert_augmented_cached(&node->ITRB, root, \ |
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leftmost, &ITPREFIX ## _augment); \ |
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} \ |
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\ |
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ITSTATIC void ITPREFIX ## _remove(ITSTRUCT *node, \ |
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struct rb_root_cached *root) \ |
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{ \ |
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rb_erase_augmented_cached(&node->ITRB, root, &ITPREFIX ## _augment); \ |
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} \ |
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\ |
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/* \ |
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* Iterate over intervals intersecting [start;last] \ |
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* \ |
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* Note that a node's interval intersects [start;last] iff: \ |
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* Cond1: ITSTART(node) <= last \ |
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* and \ |
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* Cond2: start <= ITLAST(node) \ |
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*/ \ |
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\ |
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static ITSTRUCT * \ |
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ITPREFIX ## _subtree_search(ITSTRUCT *node, ITTYPE start, ITTYPE last) \ |
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{ \ |
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while (true) { \ |
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/* \ |
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* Loop invariant: start <= node->ITSUBTREE \ |
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* (Cond2 is satisfied by one of the subtree nodes) \ |
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*/ \ |
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if (node->ITRB.rb_left) { \ |
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ITSTRUCT *left = rb_entry(node->ITRB.rb_left, \ |
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ITSTRUCT, ITRB); \ |
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if (start <= left->ITSUBTREE) { \ |
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/* \ |
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* Some nodes in left subtree satisfy Cond2. \ |
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* Iterate to find the leftmost such node N. \ |
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* If it also satisfies Cond1, that's the \ |
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* match we are looking for. Otherwise, there \ |
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* is no matching interval as nodes to the \ |
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* right of N can't satisfy Cond1 either. \ |
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*/ \ |
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node = left; \ |
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continue; \ |
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} \ |
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} \ |
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if (ITSTART(node) <= last) { /* Cond1 */ \ |
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if (start <= ITLAST(node)) /* Cond2 */ \ |
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return node; /* node is leftmost match */ \ |
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if (node->ITRB.rb_right) { \ |
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node = rb_entry(node->ITRB.rb_right, \ |
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ITSTRUCT, ITRB); \ |
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if (start <= node->ITSUBTREE) \ |
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continue; \ |
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} \ |
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} \ |
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return NULL; /* No match */ \ |
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} \ |
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} \ |
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\ |
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ITSTATIC ITSTRUCT * \ |
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ITPREFIX ## _iter_first(struct rb_root_cached *root, \ |
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ITTYPE start, ITTYPE last) \ |
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{ \ |
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ITSTRUCT *node, *leftmost; \ |
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\ |
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if (!root->rb_root.rb_node) \ |
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return NULL; \ |
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\ |
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/* \ |
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* Fastpath range intersection/overlap between A: [a0, a1] and \ |
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* B: [b0, b1] is given by: \ |
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* \ |
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* a0 <= b1 && b0 <= a1 \ |
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* \ |
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* ... where A holds the lock range and B holds the smallest \ |
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* 'start' and largest 'last' in the tree. For the later, we \ |
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* rely on the root node, which by augmented interval tree \ |
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* property, holds the largest value in its last-in-subtree. \ |
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* This allows mitigating some of the tree walk overhead for \ |
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* for non-intersecting ranges, maintained and consulted in O(1). \ |
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*/ \ |
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node = rb_entry(root->rb_root.rb_node, ITSTRUCT, ITRB); \ |
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if (node->ITSUBTREE < start) \ |
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return NULL; \ |
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\ |
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leftmost = rb_entry(root->rb_leftmost, ITSTRUCT, ITRB); \ |
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if (ITSTART(leftmost) > last) \ |
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return NULL; \ |
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\ |
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return ITPREFIX ## _subtree_search(node, start, last); \ |
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} \ |
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\ |
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ITSTATIC ITSTRUCT * \ |
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ITPREFIX ## _iter_next(ITSTRUCT *node, ITTYPE start, ITTYPE last) \ |
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{ \ |
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struct rb_node *rb = node->ITRB.rb_right, *prev; \ |
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\ |
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while (true) { \ |
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/* \ |
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* Loop invariants: \ |
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* Cond1: ITSTART(node) <= last \ |
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* rb == node->ITRB.rb_right \ |
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* \ |
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* First, search right subtree if suitable \ |
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*/ \ |
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if (rb) { \ |
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ITSTRUCT *right = rb_entry(rb, ITSTRUCT, ITRB); \ |
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if (start <= right->ITSUBTREE) \ |
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return ITPREFIX ## _subtree_search(right, \ |
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start, last); \ |
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} \ |
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\ |
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/* Move up the tree until we come from a node's left child */ \ |
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do { \ |
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rb = rb_parent(&node->ITRB); \ |
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if (!rb) \ |
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return NULL; \ |
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prev = &node->ITRB; \ |
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node = rb_entry(rb, ITSTRUCT, ITRB); \ |
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rb = node->ITRB.rb_right; \ |
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} while (prev == rb); \ |
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\ |
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/* Check if the node intersects [start;last] */ \ |
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if (last < ITSTART(node)) /* !Cond1 */ \ |
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return NULL; \ |
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else if (start <= ITLAST(node)) /* Cond2 */ \ |
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return node; \ |
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} \ |
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}
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