/usr/include/sdsl/rrr_vector_15.hpp is in libsdsl-dev 2.0.3-4.
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Copyright (C) 2011-2013 Simon Gog
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see http://www.gnu.org/licenses/ .
*/
/*! \file rrr_vector.hpp
\brief rrr_vector.hpp contains a specialisation of the sdsl::rrr_vector class,
with block size k=15 and lookup table access.
\author Simon Gog
*/
#ifndef INCLUDED_SDSL_RRR_VECTOR_15
#define INCLUDED_SDSL_RRR_VECTOR_15
#include "int_vector.hpp"
#include "util.hpp"
#include "rrr_helper.hpp" // for binomial helper class
#include "rrr_vector.hpp"
#include "iterators.hpp"
#include <vector>
#include <algorithm> // for next_permutation
#include <iostream>
//! Namespace for the succinct data structure library
namespace sdsl
{
// Helper class for the binomial coefficients \f$ 15 \choose k \f$
/*
* Size of lookup tables:
* * m_nr_to_bin: 64 kB = (2^15 entries x 2 bytes)
* * m_bin_to_nr: 64 kB = (2^15 entries x 2 bytes)
*/
class binomial15
{
public:
typedef uint32_t number_type;
private:
static class impl
{
public:
static const int n = 15;
static const int MAX_SIZE=32;
uint8_t m_space_for_bt[16];
uint8_t m_space_for_bt_pair[256];
uint64_t m_C[MAX_SIZE];
int_vector<16> m_nr_to_bin;
int_vector<16> m_bin_to_nr;
impl() {
m_nr_to_bin.resize(1<<n);
m_bin_to_nr.resize(1<<n);
for (int i=0, cnt=0, class_cnt=0; i<=n; ++i) {
m_C[i] = cnt;
class_cnt = 0;
std::vector<bool> b(n,0);
for (int j=0; j<i; ++j) b[n-j-1] = 1;
do {
uint32_t x=0;
for (int k=0; k<n; ++k)
x |= ((uint32_t)b[n-k-1])<<(n-1-k);
m_nr_to_bin[cnt] = x;
m_bin_to_nr[x] = class_cnt;
++cnt;
++class_cnt;
} while (next_permutation(b.begin(), b.end()));
if (class_cnt == 1)
m_space_for_bt[i] = 0;
else
m_space_for_bt[i] = bits::hi(class_cnt)+1;
}
if (n == 15) {
for (int x=0; x<256; ++x) {
m_space_for_bt_pair[x] = m_space_for_bt[x>>4] + m_space_for_bt[x&0x0F];
}
}
}
} iii;
public:
static inline uint8_t space_for_bt(uint32_t i) {
return iii.m_space_for_bt[i];
}
static inline uint32_t nr_to_bin(uint8_t k, uint32_t nr) {
return iii.m_nr_to_bin[iii.m_C[k]+nr];
}
static inline uint32_t bin_to_nr(uint32_t bin) {
return iii.m_bin_to_nr[bin];
}
static inline uint8_t space_for_bt_pair(uint8_t x) {
return iii.m_space_for_bt_pair[x];
}
};
//! A specialization of the rrr_vector class for a block_size of 15.
/*!
* \tparam t_rac Random access integer vector. Use to store the block types.
*
* Several tricks were used to speed-up the operations:
* * Whenever possible 2 4-bit blocks are decoded at once.
* * When the rank position lies in a block which consists only of zeros or
* ones (a uniform block), then we only have to sum up the values of the
* block type array between the last sampled position and the
* destination block. That can be done by using bit-parallelism on
* 64-bit words.
*/
template<class t_rac, uint16_t t_k>
class rrr_vector<15, t_rac, t_k>
{
public:
typedef bit_vector::size_type size_type;
typedef bit_vector::value_type value_type;
typedef bit_vector::difference_type difference_type;
typedef t_rac rac_type;
typedef random_access_const_iterator<rrr_vector> iterator;
typedef bv_tag index_category;
friend class rank_support_rrr<0, 15, t_rac, t_k>;
friend class rank_support_rrr<1, 15, t_rac, t_k>;
friend class select_support_rrr<0, 15, t_rac, t_k>;
friend class select_support_rrr<1, 15, t_rac, t_k>;
typedef rank_support_rrr<1, 15, t_rac, t_k> rank_1_type;
typedef rank_support_rrr<0, 15, t_rac, t_k> rank_0_type;
typedef select_support_rrr<1, 15, t_rac, t_k> select_1_type;
typedef select_support_rrr<0, 15, t_rac, t_k> select_0_type;
enum { block_size = 15 };
typedef binomial15 bi_type;
private:
size_type m_size = 0; // Size of the original bit_vector.
rac_type m_bt; // Vector for block types (bt). bt equals the
// number of set bits in the block.
bit_vector m_btnr; // Compressed block type numbers.
int_vector<> m_btnrp; // Sample pointers into m_btnr.
int_vector<> m_rank; // Sample rank values.
void copy(const rrr_vector& rrr) {
m_size = rrr.m_size;
m_bt = rrr.m_bt;
m_btnr = rrr.m_btnr;
m_btnrp = rrr.m_btnrp;
m_rank = rrr.m_rank;
}
public:
const rac_type& bt = m_bt;
const bit_vector& btnr = m_btnr;
//! Default constructor
/*! \param k Store rank samples and pointers each k-th blocks.
*/
rrr_vector() {};
//! Copy constructor
rrr_vector(const rrr_vector& rrr) {
copy(rrr);
}
//! Move constructor
rrr_vector(rrr_vector&& rrr) : m_size(std::move(rrr.m_size)),
m_bt(std::move(rrr.m_bt)),
m_btnr(std::move(rrr.m_btnr)), m_btnrp(std::move(rrr.m_btnrp)),
m_rank(std::move(rrr.m_rank)) {}
//! Constructor
/*!
* \param bv Uncompressed bitvector.
* \param k Store rank samples and pointers each k-th blocks.
*/
rrr_vector(const bit_vector& bv) {
m_size = bv.size();
int_vector<> bt_array;
bt_array = int_vector<>(m_size/block_size+1, 0, bits::hi(block_size)+1);
// (1) calculate the block types and store them in m_bt
size_type pos = 0, i = 0, x;
size_type btnr_pos = 0;
size_type sum_rank = 0;
while (pos + block_size <= m_size) { // handle all full blocks
bt_array[ i++ ] = x = bits::cnt(bv.get_int(pos, block_size));
sum_rank += x;
btnr_pos += bi_type::space_for_bt(x);
pos += block_size;
}
if (pos < m_size) { // handle last full block
bt_array[ i++ ] = x = bits::cnt(bv.get_int(pos, m_size - pos));
sum_rank += x;
btnr_pos += bi_type::space_for_bt(x);
}
m_btnr = bit_vector(std::max(btnr_pos, (size_type)64), 0); // max necessary for case: block_size == 1
m_btnrp = int_vector<>((bt_array.size()+t_k-1)/t_k, 0, bits::hi(btnr_pos)+1);
m_rank = int_vector<>((bt_array.size()+t_k-1)/t_k + ((m_size % (t_k*block_size))>0), 0, bits::hi(sum_rank)+1);
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
// only add a finishing block, if the last block of the superblock is not a dummy block
// (2) calculate block type numbers and pointers into btnr and rank samples
pos = 0; i = 0;
btnr_pos= 0, sum_rank = 0;
while (pos + block_size <= m_size) { // handle all full blocks
if ((i % t_k) == 0) {
m_btnrp[ i/t_k ] = btnr_pos;
m_rank[ i/t_k ] = sum_rank;
}
uint16_t space_for_bt = bi_type::space_for_bt(x=bt_array[i++]);
sum_rank += x;
if (space_for_bt) {
m_btnr.set_int(btnr_pos, bi_type::bin_to_nr(bv.get_int(pos, block_size)), space_for_bt);
}
btnr_pos += space_for_bt;
pos += block_size;
}
if (pos < m_size) { // handle last not full block
if ((i % t_k) == 0) {
m_btnrp[ i/t_k ] = btnr_pos;
m_rank[ i/t_k ] = sum_rank;
}
uint16_t space_for_bt = bi_type::space_for_bt(x=bt_array[i++]);
sum_rank += x;
if (space_for_bt) {
m_btnr.set_int(btnr_pos, bi_type::bin_to_nr(bv.get_int(pos, m_size - pos)), space_for_bt);
}
btnr_pos += space_for_bt;
assert(m_rank.size()-1 == ((i+t_k-1)/t_k));
} else { // handle last empty full block
assert(m_rank.size()-1 == ((i+t_k-1)/t_k));
}
// for technical reasons add an additional element to m_rank
m_rank[ m_rank.size()-1 ] = sum_rank; // sum_rank contains the total number of set bits in bv
m_bt = rac_type(std::move(bt_array));
}
//! Swap method
void swap(rrr_vector& rrr) {
if (this != &rrr) {
std::swap(m_size, rrr.m_size);
m_bt.swap(rrr.m_bt);
m_btnr.swap(rrr.m_btnr);
m_btnrp.swap(rrr.m_btnrp);
m_rank.swap(rrr.m_rank);
}
}
//! Accessing the i-th element of the original bit_vector
/*! \param i An index i with \f$ 0 \leq i < size() \f$.
\return The i-th bit of the original bit_vector
*/
value_type operator[](size_type i)const {
size_type bt_idx = i/block_size ;
uint8_t* bt = (uint8_t*)(m_bt.data());
uint32_t i_bt = *(bt + (bt_idx/2));
if (bt_idx%2 == 1) {
i_bt >>= 4;
} else {
i_bt &= 0x0F;
}
if (i_bt == 0 or i_bt == block_size) {
return i_bt > 0;
}
size_type sample_pos = bt_idx/t_k;
size_type btnrp = m_btnrp[ sample_pos ];
size_type j = (sample_pos*t_k);
bt += j/2;
if (j%2 == 1 and j < bt_idx) {
btnrp += bi_type::space_for_bt((*bt++)>>4);
++j;
}
while (j+1 < bt_idx) {
btnrp += bi_type::space_for_bt_pair(*(bt++)); // decode two entries at once
j+=2;
}
if (j < bt_idx) {
btnrp += bi_type::space_for_bt((*bt)&0x0F);
}
uint32_t btnr = m_btnr.get_int(btnrp, bi_type::space_for_bt(i_bt));
uint8_t off = (uint8_t)(i % block_size); //i - bt_idx*block_size;
return (bi_type::nr_to_bin(i_bt, btnr) >> off) & (uint32_t)1;
}
//! Get the integer value of the binary string of length len starting at position idx.
/*! \param idx Starting index of the binary representation of the integer.
* \param len Length of the binary representation of the integer. Default value is 64.
* \returns The integer value of the binary string of length len starting at position idx.
*
* \pre idx+len-1 in [0..size()-1]
* \pre len in [1..64]
*/
uint64_t get_int(size_type idx, uint8_t len=64)const {
uint64_t res = 0;
size_type bb_idx = idx/block_size; // begin block index
size_type bb_off = idx%block_size; // begin block offset
uint16_t bt = m_bt[bb_idx];
size_type sample_pos = bb_idx/t_k;
size_type eb_idx = (idx+len-1)/block_size; // end block index
if (bb_idx == eb_idx) { // extract only in one block
if (bt == 0) { // all bits are zero
res = 0;
} else if (bt == block_size) { // all bits are zero
res = bits::lo_set[len];
} else {
size_type btnrp = m_btnrp[ sample_pos ];
for (size_type j = sample_pos*t_k; j < bb_idx; ++j) {
btnrp += bi_type::space_for_bt(m_bt[j]);
}
uint32_t btnr = m_btnr.get_int(btnrp, bi_type::space_for_bt(bt));
res = (bi_type::nr_to_bin(bt, btnr) >> bb_off) & bits::lo_set[len];
}
} else { // solve multiple block case by recursion
uint8_t b_len = block_size-bb_off;
uint8_t b_len_sum = 0;
do {
res |= get_int(idx, b_len) << b_len_sum;
idx += b_len;
b_len_sum += b_len;
len -= b_len;
b_len = block_size;
b_len = std::min(len, b_len);
} while (len > 0);
}
return res;
}
//! Assignment operator
rrr_vector& operator=(const rrr_vector& rrr) {
if (this != &rrr) {
copy(rrr);
}
return *this;
}
//! Move assignment
rrr_vector& operator=(rrr_vector&& rrr) {
swap(rrr);
return *this;
}
//! Returns the size of the original bit vector.
size_type size()const {
return m_size;
}
//! Serializes the data structure into the given ostream
size_type serialize(std::ostream& out, structure_tree_node* v=nullptr, std::string name="")const {
size_type written_bytes = 0;
structure_tree_node* child = structure_tree::add_child(v, name, util::class_name(*this));
written_bytes += write_member(m_size, out, child, "size");
written_bytes += m_bt.serialize(out, child, "bt");
written_bytes += m_btnr.serialize(out, child, "btnr");
written_bytes += m_btnrp.serialize(out, child, "btnrp");
written_bytes += m_rank.serialize(out, child, "rank_samples");
structure_tree::add_size(child, written_bytes);
return written_bytes;
}
//! Loads the data structure from the given istream.
void load(std::istream& in) {
read_member(m_size, in);
m_bt.load(in);
m_btnr.load(in);
m_btnrp.load(in);
m_rank.load(in);
}
iterator begin() const {
return iterator(this, 0);
}
iterator end() const {
return iterator(this, size());
}
};
//! rank_support for the specialized rrr_vector class of block size 15.
/*! The first template parameter is the bit pattern of size one.
*/
template<uint8_t t_b, class t_rac, uint16_t t_k>
class rank_support_rrr<t_b, 15, t_rac, t_k>
{
public:
typedef rrr_vector<15, t_rac, t_k> bit_vector_type;
typedef typename bit_vector_type::size_type size_type;
typedef typename bit_vector_type::bi_type bi_type;
enum { bit_pat = t_b };
private:
const bit_vector_type* m_v; //!< Pointer to the rank supported rrr_vector
// TODO cache for sequential ranks
// mutable size_type m_last_bt;
// mutable size_type m_last_w; // store the last decoded word
// uint16_t m_space_for_bt[256];
public:
//! Standard constructor
/*! \param v Pointer to the rrr_vector, which should be supported
*/
explicit rank_support_rrr(const bit_vector_type* v=nullptr) {
set_vector(v);
}
//! Answers rank queries
/*! \param i Argument for the length of the prefix v[0..i-1], with \f$0\leq i \leq size()\f$.
\returns Number of 1-bits in the prefix [0..i-1] of the original bit_vector.
\par Time complexity
\f$ \Order{ sample\_rate of the rrr\_vector} \f$
*/
const size_type rank(size_type i)const {
size_type bt_idx = i/bit_vector_type::block_size;
size_type sample_pos = bt_idx/t_k;
size_type btnrp = m_v->m_btnrp[ sample_pos ];
size_type rank = m_v->m_rank[ sample_pos ];
if (sample_pos+1 < m_v->m_rank.size()) {
size_type diff_rank = m_v->m_rank[ sample_pos+1 ] - rank;
if (diff_rank == 0) {
return rank_support_rrr_trait<t_b>::adjust_rank(rank, i);
} else if (diff_rank == (size_type)bit_vector_type::block_size*t_k) {
return rank_support_rrr_trait<t_b>::adjust_rank(
rank + i - sample_pos*t_k*bit_vector_type::block_size, i);
}
}
uint8_t* bt = (uint8_t*)(m_v->m_bt.data());
uint8_t last_bt = *(bt + (bt_idx/2));
if (bt_idx%2 == 1) {
last_bt >>= 4;
} else {
last_bt &= 0x0F;
}
// if the final block type consists only of ones or zeros, we don't have to
// calculate the position pointer and can sum up rank in 64 bit chunks
if (last_bt == 0 or last_bt == 15) {
if (last_bt == 15)
rank += i % bit_vector_type::block_size;
size_type j = (sample_pos*t_k) << 2;
bt_idx = bt_idx << 2;
if (bt_idx == j)
return rank_support_rrr_trait<t_b>::adjust_rank(rank, i);
// now j < bt_idx
const uint64_t* bt64 = m_v->m_bt.data() + (j >> 6); // get the word of the start
uint8_t bt64_off = j & 0x3F; // get the offset in the word of the start
const uint64_t* bt64_end = m_v->m_bt.data() + (bt_idx >> 6);
uint8_t bt64_end_off = bt_idx & 0x3F;
// Case (1)
if (bt64 == bt64_end) {
uint64_t w = ((*bt64) >> bt64_off) & bits::lo_set[bt64_end_off-bt64_off];
w = (w & 0x0f0f0f0f0f0f0f0full) + ((w >> 4) & 0x0f0f0f0f0f0f0f0full);
rank += ((0x0101010101010101ull*w) >> 56);
} else { // Case (2)
uint64_t w = ((*bt64) >> bt64_off);
w = (w & 0x0f0f0f0f0f0f0f0full) + ((w >> 4) & 0x0f0f0f0f0f0f0f0full);
rank += ((0x0101010101010101ull*w) >> 56);
while ((++bt64) != bt64_end) {
w = *bt64;
w = (w & 0x0f0f0f0f0f0f0f0full) + ((w >> 4) & 0x0f0f0f0f0f0f0f0full);
rank += ((0x0101010101010101ull*w) >> 56);
}
// now bt64 == bt64_end
if (bt64_end_off > 0) {
w = *bt64 << (64 - bt64_end_off);
w = (w & 0x0f0f0f0f0f0f0f0full) + ((w >> 4) & 0x0f0f0f0f0f0f0f0full);
rank += ((0x0101010101010101ull*w) >> 56);
}
}
return rank_support_rrr_trait<t_b>::adjust_rank(rank, i); // necessary
}
size_type j = sample_pos*t_k;
bt += j/2;
if (j%2 == 1 and j < bt_idx) {
const uint8_t r = (*bt++)>>4;
rank += r;
btnrp += bi_type::space_for_bt(r);
++j;
}
while (j+1 < bt_idx) {
const uint8_t r = *(bt++);
rank += (r>>4)+(r&0x0F);
btnrp += bi_type::space_for_bt_pair(r); // decode two entries at once
j+=2;
}
if (j < bt_idx) {
const uint8_t r = (*bt);
rank += r&0x0F;
btnrp += bi_type::space_for_bt(r&0x0F);
++j;
}
uint8_t off = i % bit_vector_type::block_size; //i - bt_idx*bit_vector_type::block_size;
if (!off) { // needed for special case: if i=size() is a multiple of block_size
// the access to m_bt would cause a invalid memory access
return rank_support_rrr_trait<t_b>::adjust_rank(rank, i);
}
uint32_t btnr = m_v->m_btnr.get_int(btnrp, bi_type::space_for_bt(last_bt));
return rank_support_rrr_trait<t_b>::adjust_rank(rank +
bits::cnt(((uint64_t)(bi_type::nr_to_bin(last_bt, btnr))) & bits::lo_set[off]), i);
}
//! Short hand for rank(i)
const size_type operator()(size_type i)const {
return rank(i);
}
//! Returns the size of the original vector
const size_type size()const {
return m_v->size();
}
//! Set the supported vector.
void set_vector(const bit_vector_type* v=nullptr) {
m_v = v;
}
rank_support_rrr& operator=(const rank_support_rrr& rs) {
if (this != &rs) {
set_vector(rs.m_v);
}
return *this;
}
void swap(rank_support_rrr&) { }
//! Load the data structure from a stream and set the supported vector.
void load(std::istream&, const bit_vector_type* v=nullptr) {
set_vector(v);
}
//! Serializes the data structure into a stream.
size_type serialize(std::ostream&, structure_tree_node* v=nullptr, std::string name="")const {
structure_tree_node* child = structure_tree::add_child(v, name, util::class_name(*this));
structure_tree::add_size(child, 0);
return 0;
}
};
//! Select support for the specialized rrr_vector class of block size 15.
template<uint8_t t_b, class t_rac, uint16_t t_k>
class select_support_rrr<t_b, 15, t_rac, t_k>
{
public:
typedef rrr_vector<15, t_rac, t_k> bit_vector_type;
typedef typename bit_vector_type::size_type size_type;
typedef typename bit_vector_type::bi_type bi_type;
enum { bit_pat = t_b };
private:
const bit_vector_type* m_v; //!< Pointer to the rank supported rrr_vector
// TODO: hinted binary search
size_type select1(size_type i)const {
if (m_v->m_rank[m_v->m_rank.size()-1] < i)
return size();
// (1) binary search for the answer in the rank_samples
size_type begin=0, end=m_v->m_rank.size()-1; // min included, max excluded
size_type idx, rank;
// invariant: m_rank[end] >= i
// m_rank[begin] < i
while (end-begin > 1) {
idx = (begin+end) >> 1; // idx in [0..m_rank.size()-1]
rank = m_v->m_rank[idx];
if (rank >= i)
end = idx;
else { // rank < i
begin = idx;
}
}
// (2) linear search between the samples
rank = m_v->m_rank[begin]; // now i>rank
idx = begin * t_k; // initialize idx for select result
size_type diff_rank = m_v->m_rank[end] - rank;
if (diff_rank == (size_type)bit_vector_type::block_size*t_k) {// optimisation for select<1>
return idx*bit_vector_type::block_size + i-rank -1;
}
size_type btnrp = m_v->m_btnrp[ begin ];
uint8_t bt = 0, s = 0; // temp variables for block_type and space for block type
while (i > rank) {
bt = m_v->m_bt[idx++];
rank += bt;
btnrp += (s=bi_type::space_for_bt(bt));
}
rank -= bt;
uint32_t btnr = m_v->m_btnr.get_int(btnrp-s, s);
return (idx-1) * bit_vector_type::block_size + bits::sel(bi_type::nr_to_bin(bt, btnr), i-rank);
}
// TODO: hinted binary search
size_type select0(size_type i)const {
if ((size()-m_v->m_rank[m_v->m_rank.size()-1]) < i)
return size();
// (1) binary search for the answer in the rank_samples
size_type begin=0, end=m_v->m_rank.size()-1; // min included, max excluded
size_type idx, rank;
// invariant: m_rank[end] >= i
// m_rank[begin] < i
while (end-begin > 1) {
idx = (begin+end) >> 1; // idx in [0..m_rank.size()-1]
rank = idx*bit_vector_type::block_size*t_k - m_v->m_rank[idx];
if (rank >= i)
end = idx;
else { // rank < i
begin = idx;
}
}
// (2) linear search between the samples
rank = begin*bit_vector_type::block_size*t_k - m_v->m_rank[begin]; // now i>rank
idx = begin * t_k; // initialize idx for select result
if (m_v->m_rank[end] == m_v->m_rank[begin]) { // only for select<0>
return idx*bit_vector_type::block_size + i-rank -1;
}
size_type btnrp = m_v->m_btnrp[ begin ];
uint8_t bt = 0, s = 0; // temp variables for block_type and space for block type
while (i > rank) {
bt = m_v->m_bt[idx++];
rank += (bit_vector_type::block_size-bt);
btnrp += (s=bi_type::space_for_bt(bt));
}
rank -= (bit_vector_type::block_size-bt);
uint32_t btnr = m_v->m_btnr.get_int(btnrp-s, s);
return (idx-1) * bit_vector_type::block_size + bits::sel(~((uint64_t)bi_type::nr_to_bin(bt, btnr)), i-rank);
}
public:
select_support_rrr(const bit_vector_type* v=nullptr) {
set_vector(v);
}
//! Answers select queries
size_type select(size_type i)const {
return t_b ? select1(i) : select0(i);
}
const size_type operator()(size_type i)const {
return select(i);
}
const size_type size()const {
return m_v->size();
}
void set_vector(const bit_vector_type* v=nullptr) {
m_v = v;
}
select_support_rrr& operator=(const select_support_rrr& rs) {
if (this != &rs) {
set_vector(rs.m_v);
}
return *this;
}
void swap(select_support_rrr&) { }
void load(std::istream&, const bit_vector_type* v=nullptr) {
set_vector(v);
}
size_type serialize(std::ostream&, structure_tree_node* v=nullptr, std::string name="")const {
structure_tree_node* child = structure_tree::add_child(v, name, util::class_name(*this));
structure_tree::add_size(child, 0);
return 0;
}
};
}// end namespace sdsl
#endif
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