+
+
+
+
+
+
+
+
+
+
+
+
+
Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula.
+More...
+
#include <iostream>
+#include <cassert>
+
+ |
+| uint64_t | math::largestPower (uint32_t n, const uint16_t &p) |
+| | Function to calculate largest power. More...
|
+| |
+| static void | test () |
+| | Function for testing largestPower function. test cases and assert statement. More...
|
+| |
+| int | main () |
+| | Main function. More...
|
+| |
+
+
+
Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula.
+
Given an integer n and a prime number p, the task is to find the largest x such that p^x (p raised to power x) divides n! (factorial). This will be done using Legendre's formula: x = [n/(p^1)] + [n/(p^2)] + [n/(p^3)] + \ldots + 1
- See also
- more on https://math.stackexchange.com/questions/141196/highest-power-of-a-prime-p-dividing-n
+
- Author
- uday6670
+
+
+
◆ main()
+
+
+
+
+
+ | int main |
+ ( |
+ void |
+ | ) |
+ |
+
+
+
+
+
Main function.
+
- Returns
- 0 on exit
+
+
+
+
+
+
+
◆ test()
+
+
+
+
+
+
+
+
+ | static void test |
+ ( |
+ | ) |
+ |
+
+
+ |
+
+static |
+
+
+
+
+
Function for testing largestPower function. test cases and assert statement.
+
- Returns
void
+
+
+
50 assert(test_case_1==3);
+
+
+
+
54 assert(test_case_2==4);
+
+
+
+
58 assert(test_case_3==6);
+
+
+
+
62 assert(test_case_4==23);
+
+
+
+
66 assert(test_case_5==2);
+
+
+
+
+
+
+
+
+
|
+| uint64_t | largestPower (uint32_t n, const uint16_t &p) |
+| | Function to calculate largest power. More...
|
+| |
| uint64_t | lcmSum (const uint16_t &num) |
| |
| bool | magic_number (const uint64_t &n) |
@@ -120,8 +123,11 @@ Functions
for std::vector
for std::cin and std::cout
for io operations
+
for assert
for assert for std::cin and std::cout
Mathematical algorithms
+
for std::cin and std::cout
+
Mathematical algorithms
for assert
Mathematical algorithms
for assert for io operations
@@ -156,6 +162,56 @@ Functions
◆ largestPower()
+
+
+
+
+
+ | uint64_t math::largestPower |
+ ( |
+ uint32_t |
+ n, |
+
+
+ |
+ |
+ const uint16_t & |
+ p |
+
+
+ |
+ ) |
+ | |
+
+
+
+
+
Function to calculate largest power.
+
- Parameters
-
+
+ | n | number |
+ | p | prime number |
+
+
+
+
- Returns
- largest power
+
+
+
◆ lcmSum()
diff --git a/dir_296d53ceaeaa7e099814a6def439fe8a.html b/dir_296d53ceaeaa7e099814a6def439fe8a.html
index 92e4e42a5..be563de0b 100644
--- a/dir_296d53ceaeaa7e099814a6def439fe8a.html
+++ b/dir_296d53ceaeaa7e099814a6def439fe8a.html
@@ -157,6 +157,9 @@ Files
| file | large_number.h [code] |
| | Library to perform arithmatic operations on arbitrarily large numbers.
|
| |
+| file | largest_power.cpp |
+| | Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula.
|
+| |
| file | lcm_sum.cpp |
| | An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\).
|
| |
diff --git a/dir_296d53ceaeaa7e099814a6def439fe8a.js b/dir_296d53ceaeaa7e099814a6def439fe8a.js
index 98049f139..3a98297cf 100644
--- a/dir_296d53ceaeaa7e099814a6def439fe8a.js
+++ b/dir_296d53ceaeaa7e099814a6def439fe8a.js
@@ -22,6 +22,7 @@ var dir_296d53ceaeaa7e099814a6def439fe8a =
[ "large_number.h", "d4/d86/large__number_8h.html", [
[ "large_number", "db/d82/classlarge__number.html", "db/d82/classlarge__number" ]
] ],
+ [ "largest_power.cpp", "d5/d7a/largest__power_8cpp.html", "d5/d7a/largest__power_8cpp" ],
[ "lcm_sum.cpp", "d5/d83/lcm__sum_8cpp.html", "d5/d83/lcm__sum_8cpp" ],
[ "least_common_multiple.cpp", "d4/d21/least__common__multiple_8cpp.html", "d4/d21/least__common__multiple_8cpp" ],
[ "magic_number.cpp", "d9/d44/magic__number_8cpp.html", "d9/d44/magic__number_8cpp" ],
diff --git a/files.html b/files.html
index ddb4cf59d..0287d0d68 100644
--- a/files.html
+++ b/files.html
@@ -189,25 +189,26 @@ solve-a-rat-in-a-maze-c-java-pytho/">Rat in a Maze algorithm
| gcd_recursive_euclidean.cpp | Compute the greatest common denominator of two integers using recursive form of Euclidean algorithm |
| large_factorial.cpp | Compute factorial of any arbitratily large number/ |
| large_number.h | Library to perform arithmatic operations on arbitrarily large numbers |
-| lcm_sum.cpp | An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) |
-| least_common_multiple.cpp | |
-| magic_number.cpp | A simple program to check if the given number is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number |
-| miller_rabin.cpp | |
-| modular_exponentiation.cpp | C++ Program for Modular Exponentiation Iteratively |
-| modular_inverse_fermat_little_theorem.cpp | C++ Program to find the modular inverse using Fermat's Little Theorem |
-| n_choose_r.cpp | Combinations n choose r function implementation |
-| ncr_modulo_p.cpp | This program aims at calculating nCr modulo p |
-| number_of_positive_divisors.cpp | C++ Program to calculate the number of positive divisors |
-| power_for_huge_numbers.cpp | Compute powers of large numbers |
-| prime_factorization.cpp | Prime factorization of positive integers |
-| prime_numbers.cpp | Get list of prime numbers |
-| primes_up_to_billion.cpp | Compute prime numbers upto 1 billion |
-| realtime_stats.cpp | Compute statistics for data entered in rreal-time |
-| sieve_of_eratosthenes.cpp | Get list of prime numbers using Sieve of Eratosthenes |
-| sqrt_double.cpp | Calculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using bisection method of root-finding |
-| string_fibonacci.cpp | This Programme returns the Nth fibonacci as a string |
-| sum_of_binomial_coefficient.cpp | Algorithm to find sum of binomial coefficients of a given positive integer |
-| sum_of_digits.cpp | A C++ Program to find the Sum of Digits of input integer |
+| largest_power.cpp | Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula |
+| lcm_sum.cpp | An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) |
+| least_common_multiple.cpp | |
+| magic_number.cpp | A simple program to check if the given number is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number |
+| miller_rabin.cpp | |
+| modular_exponentiation.cpp | C++ Program for Modular Exponentiation Iteratively |
+| modular_inverse_fermat_little_theorem.cpp | C++ Program to find the modular inverse using Fermat's Little Theorem |
+| n_choose_r.cpp | Combinations n choose r function implementation |
+| ncr_modulo_p.cpp | This program aims at calculating nCr modulo p |
+| number_of_positive_divisors.cpp | C++ Program to calculate the number of positive divisors |
+| power_for_huge_numbers.cpp | Compute powers of large numbers |
+| prime_factorization.cpp | Prime factorization of positive integers |
+| prime_numbers.cpp | Get list of prime numbers |
+| primes_up_to_billion.cpp | Compute prime numbers upto 1 billion |
+| realtime_stats.cpp | Compute statistics for data entered in rreal-time |
+| sieve_of_eratosthenes.cpp | Get list of prime numbers using Sieve of Eratosthenes |
+| sqrt_double.cpp | Calculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using bisection method of root-finding |
+| string_fibonacci.cpp | This Programme returns the Nth fibonacci as a string |
+| sum_of_binomial_coefficient.cpp | Algorithm to find sum of binomial coefficients of a given positive integer |
+| sum_of_digits.cpp | A C++ Program to find the Sum of Digits of input integer |
| ► numerical_methods | |
| bisection_method.cpp | Solve the equation \(f(x)=0\) using bisection method |
| brent_method_extrema.cpp | Find real extrema of a univariate real function in a given interval using Brent's method |
diff --git a/globals_func_m.html b/globals_func_m.html
index b2be8ca27..b680b40db 100644
--- a/globals_func_m.html
+++ b/globals_func_m.html
@@ -101,14 +101,14 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl
, linked_list.cpp
, bidirectional_dijkstra.cpp
, fibonacci.cpp
+, binary_search.cpp
, exponential_search.cpp
-, fibonacci_search.cpp
, fibonacci_fast.cpp
+, fibonacci_search.cpp
, hash_search.cpp
-, interpolation_search.cpp
, breadth_first_search.cpp
, fibonacci_sum.cpp
-, interpolation_search2.cpp
+, interpolation_search.cpp
, rabin_karp.cpp
, knuth_morris_pratt.cpp
, horspool.cpp
@@ -129,15 +129,15 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl
, comb_sort.cpp
, bogo_sort.cpp
, text_search.cpp
-, linear_search.cpp
-, gcd_iterative_euclidean.cpp
-, median_search.cpp
, ternary_search.cpp
+, interpolation_search2.cpp
+, gcd_iterative_euclidean.cpp
+, linear_search.cpp
+, median_search.cpp
, linkedlist_implentation_usingarray.cpp
, connected_components.cpp
, gcd_of_n_numbers.cpp
, gcd_recursive_euclidean.cpp
-, binary_search.cpp
, sparse_table.cpp
, heavy_light_decomposition.cpp
, fenwick_tree.cpp
@@ -193,9 +193,10 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl
, miller_rabin.cpp
, magic_number.cpp
, least_common_multiple.cpp
+, lcm_sum.cpp
, depth_first_search.cpp
, large_factorial.cpp
-, lcm_sum.cpp
+, largest_power.cpp
, caesar_cipher.cpp
, queue_using_array.cpp
, dijkstra.cpp
diff --git a/globals_func_t.html b/globals_func_t.html
index fa46410ff..9a31bb666 100644
--- a/globals_func_t.html
+++ b/globals_func_t.html
@@ -101,21 +101,22 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
, morse_code.cpp
, 0_1_knapsack.cpp
, jumpgame.cpp
+, median_search.cpp
, bogo_sort.cpp
-, cycle_sort.cpp
, gram_schmidt.cpp
+, cycle_sort.cpp
, gnome_sort.cpp
-, heap_sort.cpp
, coin_change_topdown.cpp
, neural_network.cpp
+, heap_sort.cpp
, merge_insertion_sort.cpp
-, pancake_sort.cpp
, armstrong_number.cpp
+, pancake_sort.cpp
, strand_sort.cpp
-, wiggle_sort.cpp
, vigenere_cipher.cpp
, cut_rod.cpp
, check_amicable_pair.cpp
+, wiggle_sort.cpp
, horspool.cpp
, double_factorial.cpp
, palindrome_partitioning.cpp
@@ -124,18 +125,18 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
, caesar_cipher.cpp
, xor_cipher.cpp
, shortest_common_supersequence.cpp
+, largest_power.cpp
, lcm_sum.cpp
-, modular_exponentiation.cpp
, word_break.cpp
+, modular_exponentiation.cpp
, n_choose_r.cpp
-, sum_of_binomial_coefficient.cpp
, trie_tree.cpp
, jarvis_algorithm.cpp
+, sum_of_binomial_coefficient.cpp
, sum_of_digits.cpp
-, rungekutta.cpp
, is_graph_bipartite.cpp
+, rungekutta.cpp
, smallest_circle.cpp
-, median_search.cpp
test1()
: hill_cipher.cpp
@@ -152,36 +153,36 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
, qr_eigen_values.cpp
test2()
-: qr_eigen_values.cpp
+: lu_decompose.cpp
+, qr_eigen_values.cpp
, smallest_circle.cpp
-, lu_decompose.cpp
-, sum_of_digits.cpp
+, large_factorial.cpp
+, golden_search_extrema.cpp
, hill_cipher.cpp
, hamiltons_cycle.cpp
, adaline_learning.cpp
, kohonen_som_topology.cpp
, kohonen_som_trace.cpp
-, large_factorial.cpp
+, sum_of_digits.cpp
, brent_method_extrema.cpp
, durand_kerner_roots.cpp
-, golden_search_extrema.cpp
test3()
: hamiltons_cycle.cpp
, adaline_learning.cpp
, kohonen_som_topology.cpp
, kohonen_som_trace.cpp
-, brent_method_extrema.cpp
-, smallest_circle.cpp
, golden_search_extrema.cpp
+, smallest_circle.cpp
+, brent_method_extrema.cpp
test_1()
: heavy_light_decomposition.cpp
, pigeonhole_sort.cpp
test_2()
-: pigeonhole_sort.cpp
-, heavy_light_decomposition.cpp
+: heavy_light_decomposition.cpp
+, pigeonhole_sort.cpp
test_2d_classes()
: kohonen_som_topology.cpp
@@ -225,24 +226,24 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
: kohonen_som_trace.cpp
tests()
-: radix_sort2.cpp
-, connected_components.cpp
-, check_factorial.cpp
-, dijkstra.cpp
-, number_of_positive_divisors.cpp
-, insertion_sort.cpp
-, magic_number.cpp
-, sieve_of_eratosthenes.cpp
+: number_of_positive_divisors.cpp
, bidirectional_dijkstra.cpp
-, lowest_common_ancestor.cpp
-, comb_sort.cpp
-, hopcroft_karp.cpp
-, complex_numbers.cpp
-, least_common_multiple.cpp
-, breadth_first_search.cpp
, double_factorial.cpp
-, miller_rabin.cpp
+, magic_number.cpp
+, radix_sort2.cpp
+, breadth_first_search.cpp
+, comb_sort.cpp
+, sieve_of_eratosthenes.cpp
+, dijkstra.cpp
+, lowest_common_ancestor.cpp
+, connected_components.cpp
+, insertion_sort.cpp
+, least_common_multiple.cpp
+, check_factorial.cpp
, ncr_modulo_p.cpp
+, complex_numbers.cpp
+, miller_rabin.cpp
+, hopcroft_karp.cpp
TH()
: tower_of_hanoi.cpp
diff --git a/globals_i.html b/globals_i.html
index 9a4c725b7..951efb841 100644
--- a/globals_i.html
+++ b/globals_i.html
@@ -126,14 +126,14 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
is_square()
: ordinary_least_squares_regressor.cpp
-IsPrime()
-: primality_test.cpp
+isprime
+: prime_factorization.cpp
isPrime()
: modular_inverse_fermat_little_theorem.cpp
-isprime
-: prime_factorization.cpp
+IsPrime()
+: primality_test.cpp
it_ternary_search()
: ternary_search.cpp
diff --git a/globals_m.html b/globals_m.html
index b1924791e..b6fc97cd1 100644
--- a/globals_m.html
+++ b/globals_m.html
@@ -101,25 +101,25 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, linked_list.cpp
, bidirectional_dijkstra.cpp
, fibonacci.cpp
+, binary_search.cpp
, exponential_search.cpp
-, fibonacci_search.cpp
, fibonacci_fast.cpp
+, fibonacci_search.cpp
, hash_search.cpp
-, interpolation_search.cpp
, breadth_first_search.cpp
, fibonacci_sum.cpp
+, interpolation_search.cpp
, interpolation_search2.cpp
-, linear_search.cpp
, gcd_iterative_euclidean.cpp
+, linear_search.cpp
, median_search.cpp
-, ternary_search.cpp
, linkedlist_implentation_usingarray.cpp
, connected_components.cpp
, gcd_of_n_numbers.cpp
+, ternary_search.cpp
, text_search.cpp
-, bogo_sort.cpp
, gcd_recursive_euclidean.cpp
-, comb_sort.cpp
+, bogo_sort.cpp
, rabin_karp.cpp
, knuth_morris_pratt.cpp
, horspool.cpp
@@ -134,21 +134,21 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, merge_sort.cpp
, merge_insertion_sort.cpp
, insertion_sort.cpp
-, cycle_sort.cpp
+, heap_sort.cpp
+, comb_sort.cpp
, depth_first_search.cpp
, large_factorial.cpp
+, cycle_sort.cpp
, gnome_sort.cpp
-, heap_sort.cpp
-, lcm_sum.cpp
+, largest_power.cpp
, caesar_cipher.cpp
, queue_using_array.cpp
, dijkstra.cpp
+, lcm_sum.cpp
, least_common_multiple.cpp
-, magic_number.cpp
, hamiltons_cycle.cpp
+, magic_number.cpp
, miller_rabin.cpp
-, modular_exponentiation.cpp
-, binary_search.cpp
, sparse_table.cpp
, heavy_light_decomposition.cpp
, fenwick_tree.cpp
@@ -198,10 +198,11 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, power_for_huge_numbers.cpp
, number_of_positive_divisors.cpp
, ncr_modulo_p.cpp
+, n_choose_r.cpp
, queue_using_two_stacks.cpp
, hopcroft_karp.cpp
+, modular_exponentiation.cpp
, modular_inverse_fermat_little_theorem.cpp
-, n_choose_r.cpp
, is_graph_bipartite.cpp
, n_queens_all_solution_optimised.cpp
, hill_cipher.cpp
diff --git a/globals_t.html b/globals_t.html
index 43da94249..2e8b32385 100644
--- a/globals_t.html
+++ b/globals_t.html
@@ -101,21 +101,22 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
, morse_code.cpp
, 0_1_knapsack.cpp
, jumpgame.cpp
+, median_search.cpp
, bogo_sort.cpp
-, cycle_sort.cpp
, gram_schmidt.cpp
+, cycle_sort.cpp
, gnome_sort.cpp
-, heap_sort.cpp
, coin_change_topdown.cpp
, neural_network.cpp
+, heap_sort.cpp
, merge_insertion_sort.cpp
-, pancake_sort.cpp
, armstrong_number.cpp
+, pancake_sort.cpp
, strand_sort.cpp
-, wiggle_sort.cpp
, vigenere_cipher.cpp
, cut_rod.cpp
, check_amicable_pair.cpp
+, wiggle_sort.cpp
, horspool.cpp
, double_factorial.cpp
, palindrome_partitioning.cpp
@@ -124,18 +125,18 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
, caesar_cipher.cpp
, xor_cipher.cpp
, shortest_common_supersequence.cpp
+, largest_power.cpp
, lcm_sum.cpp
-, modular_exponentiation.cpp
, word_break.cpp
+, modular_exponentiation.cpp
, n_choose_r.cpp
-, sum_of_binomial_coefficient.cpp
, trie_tree.cpp
, jarvis_algorithm.cpp
+, sum_of_binomial_coefficient.cpp
, sum_of_digits.cpp
-, rungekutta.cpp
, is_graph_bipartite.cpp
+, rungekutta.cpp
, smallest_circle.cpp
-, median_search.cpp
test1()
: hill_cipher.cpp
@@ -152,43 +153,43 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
, qr_eigen_values.cpp
test2()
-: lu_decompose.cpp
+: golden_search_extrema.cpp
+, lu_decompose.cpp
, qr_eigen_values.cpp
, smallest_circle.cpp
+, large_factorial.cpp
, hill_cipher.cpp
-, sum_of_digits.cpp
, hamiltons_cycle.cpp
, adaline_learning.cpp
, kohonen_som_topology.cpp
, kohonen_som_trace.cpp
-, large_factorial.cpp
+, sum_of_digits.cpp
, brent_method_extrema.cpp
, durand_kerner_roots.cpp
-, golden_search_extrema.cpp
test3()
: hamiltons_cycle.cpp
, adaline_learning.cpp
, kohonen_som_topology.cpp
, kohonen_som_trace.cpp
-, brent_method_extrema.cpp
-, smallest_circle.cpp
, golden_search_extrema.cpp
+, smallest_circle.cpp
+, brent_method_extrema.cpp
test_1()
: heavy_light_decomposition.cpp
, pigeonhole_sort.cpp
test_2()
-: pigeonhole_sort.cpp
-, heavy_light_decomposition.cpp
+: heavy_light_decomposition.cpp
+, pigeonhole_sort.cpp
test_2d_classes()
: kohonen_som_topology.cpp
test_3()
-: pigeonhole_sort.cpp
-, heavy_light_decomposition.cpp
+: heavy_light_decomposition.cpp
+, pigeonhole_sort.cpp
test_3d_classes()
: kohonen_som_trace.cpp
@@ -229,21 +230,21 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
tests()
: hopcroft_karp.cpp
-, radix_sort2.cpp
-, double_factorial.cpp
-, bidirectional_dijkstra.cpp
-, number_of_positive_divisors.cpp
-, connected_components.cpp
-, comb_sort.cpp
-, sieve_of_eratosthenes.cpp
, check_factorial.cpp
-, least_common_multiple.cpp
, dijkstra.cpp
-, insertion_sort.cpp
-, magic_number.cpp
-, breadth_first_search.cpp
, ncr_modulo_p.cpp
+, sieve_of_eratosthenes.cpp
+, number_of_positive_divisors.cpp
+, comb_sort.cpp
+, breadth_first_search.cpp
+, bidirectional_dijkstra.cpp
+, least_common_multiple.cpp
+, magic_number.cpp
+, radix_sort2.cpp
+, connected_components.cpp
, complex_numbers.cpp
+, double_factorial.cpp
+, insertion_sort.cpp
, miller_rabin.cpp
, lowest_common_ancestor.cpp
diff --git a/namespacemembers.html b/namespacemembers.html
index ef28de730..e5f675dc0 100644
--- a/namespacemembers.html
+++ b/namespacemembers.html
@@ -237,6 +237,9 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- l -
+- largestPower()
+: math
+
- lcmSum()
: math
diff --git a/namespacemembers_func.html b/namespacemembers_func.html
index d3219499a..e9bd232a3 100644
--- a/namespacemembers_func.html
+++ b/namespacemembers_func.html
@@ -237,6 +237,9 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
- l -
+- largestPower()
+: math
+
- lcmSum()
: math
diff --git a/navtreedata.js b/navtreedata.js
index d2ace48d9..67cbc50a1 100644
--- a/navtreedata.js
+++ b/navtreedata.js
@@ -125,10 +125,10 @@ var NAVTREEINDEX =
"annotated.html",
"d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe",
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