Documentation for 5eadfed90a4d8673d01bc1cc12b636b9a50cd817

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@@ -185,33 +185,34 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
<tr id="row_11_11_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d89/fibonacci_8cpp.html" target="_self">fibonacci.cpp</a></td><td class="desc">Generate fibonacci sequence </td></tr>
<tr id="row_11_12_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d32/fibonacci__fast_8cpp.html" target="_self">fibonacci_fast.cpp</a></td><td class="desc">Faster computation of Fibonacci series </td></tr>
<tr id="row_11_13_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/de4/fibonacci__large_8cpp.html" target="_self">fibonacci_large.cpp</a></td><td class="desc">Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library to perform additions and other operations </td></tr>
<tr id="row_11_14_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/dc3/fibonacci__sum_8cpp.html" target="_self">fibonacci_sum.cpp</a></td><td class="desc">An algorithm to calculate the sum of <a href="https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci Sequence</a>: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\) </td></tr>
<tr id="row_11_15_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/da0/gcd__iterative__euclidean_8cpp.html" target="_self">gcd_iterative_euclidean.cpp</a></td><td class="desc">Compute the greatest common denominator of two integers using <em>iterative form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm">Euclidean algorithm</a> </td></tr>
<tr id="row_11_16_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/d11/gcd__of__n__numbers_8cpp.html" target="_self">gcd_of_n_numbers.cpp</a></td><td class="desc">This program aims at calculating the GCD of n numbers by division method </td></tr>
<tr id="row_11_17_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d45/gcd__recursive__euclidean_8cpp.html" target="_self">gcd_recursive_euclidean.cpp</a></td><td class="desc">Compute the greatest common denominator of two integers using <em>recursive form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm">Euclidean algorithm</a> </td></tr>
<tr id="row_11_18_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d9d/large__factorial_8cpp.html" target="_self">large_factorial.cpp</a></td><td class="desc">Compute factorial of any arbitratily large number/ </td></tr>
<tr id="row_11_19_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><a href="d4/d86/large__number_8h_source.html"><span class="icondoc"></span></a><a class="el" href="d4/d86/large__number_8h.html" target="_self">large_number.h</a></td><td class="desc">Library to perform arithmatic operations on arbitrarily large numbers </td></tr>
<tr id="row_11_20_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d7a/largest__power_8cpp.html" target="_self">largest_power.cpp</a></td><td class="desc">Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula </td></tr>
<tr id="row_11_21_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d83/lcm__sum_8cpp.html" target="_self">lcm_sum.cpp</a></td><td class="desc">An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) </td></tr>
<tr id="row_11_22_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d21/least__common__multiple_8cpp.html" target="_self">least_common_multiple.cpp</a></td><td class="desc"></td></tr>
<tr id="row_11_23_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d44/magic__number_8cpp.html" target="_self">magic_number.cpp</a></td><td class="desc">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 </td></tr>
<tr id="row_11_24_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d42/miller__rabin_8cpp.html" target="_self">miller_rabin.cpp</a></td><td class="desc"></td></tr>
<tr id="row_11_25_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/d72/modular__division_8cpp.html" target="_self">modular_division.cpp</a></td><td class="desc">An algorithm to divide two numbers under modulo p <a href="https://www.geeksforgeeks.org/modular-division">Modular Division</a> </td></tr>
<tr id="row_11_26_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d6d/modular__exponentiation_8cpp.html" target="_self">modular_exponentiation.cpp</a></td><td class="desc">C++ Program for Modular Exponentiation Iteratively </td></tr>
<tr id="row_11_27_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html" target="_self">modular_inverse_fermat_little_theorem.cpp</a></td><td class="desc">C++ Program to find the modular inverse using <a href="https://en.wikipedia.org/wiki/Fermat%27s_little_theorem">Fermat's Little Theorem</a> </td></tr>
<tr id="row_11_28_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/dbb/n__choose__r_8cpp.html" target="_self">n_choose_r.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Combination">Combinations</a> n choose r function implementation </td></tr>
<tr id="row_11_29_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/dab/ncr__modulo__p_8cpp.html" target="_self">ncr_modulo_p.cpp</a></td><td class="desc">This program aims at calculating <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html">nCr modulo p</a> </td></tr>
<tr id="row_11_30_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html" target="_self">number_of_positive_divisors.cpp</a></td><td class="desc">C++ Program to calculate the number of positive divisors </td></tr>
<tr id="row_11_31_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/def/power__for__huge__numbers_8cpp.html" target="_self">power_for_huge_numbers.cpp</a></td><td class="desc">Compute powers of large numbers </td></tr>
<tr id="row_11_32_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d0d/prime__factorization_8cpp.html" target="_self">prime_factorization.cpp</a></td><td class="desc">Prime factorization of positive integers </td></tr>
<tr id="row_11_33_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d9b/prime__numbers_8cpp.html" target="_self">prime_numbers.cpp</a></td><td class="desc">Get list of prime numbers </td></tr>
<tr id="row_11_34_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html" target="_self">primes_up_to_billion.cpp</a></td><td class="desc">Compute prime numbers upto 1 billion </td></tr>
<tr id="row_11_35_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d08/realtime__stats_8cpp.html" target="_self">realtime_stats.cpp</a></td><td class="desc">Compute statistics for data entered in rreal-time </td></tr>
<tr id="row_11_36_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html" target="_self">sieve_of_eratosthenes.cpp</a></td><td class="desc">Get list of prime numbers using Sieve of Eratosthenes </td></tr>
<tr id="row_11_37_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="da/d24/sqrt__double_8cpp.html" target="_self">sqrt_double.cpp</a></td><td class="desc">Calculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using <a href="https://en.wikipedia.org/wiki/Bisection_method">bisection method</a> of root-finding </td></tr>
<tr id="row_11_38_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d47/string__fibonacci_8cpp.html" target="_self">string_fibonacci.cpp</a></td><td class="desc">This Programme returns the Nth fibonacci as a string </td></tr>
<tr id="row_11_39_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9d/sum__of__binomial__coefficient_8cpp.html" target="_self">sum_of_binomial_coefficient.cpp</a></td><td class="desc">Algorithm to find sum of binomial coefficients of a given positive integer </td></tr>
<tr id="row_11_40_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d83/sum__of__digits_8cpp.html" target="_self">sum_of_digits.cpp</a></td><td class="desc">A C++ Program to find the Sum of Digits of input integer </td></tr>
<tr id="row_11_14_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="da/dc9/fibonacci__matrix__exponentiation_8cpp.html" target="_self">fibonacci_matrix_exponentiation.cpp</a></td><td class="desc">This program computes the N^th Fibonacci number in modulo mod input argument </td></tr>
<tr id="row_11_15_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/dc3/fibonacci__sum_8cpp.html" target="_self">fibonacci_sum.cpp</a></td><td class="desc">An algorithm to calculate the sum of <a href="https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci Sequence</a>: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\) </td></tr>
<tr id="row_11_16_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/da0/gcd__iterative__euclidean_8cpp.html" target="_self">gcd_iterative_euclidean.cpp</a></td><td class="desc">Compute the greatest common denominator of two integers using <em>iterative form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm">Euclidean algorithm</a> </td></tr>
<tr id="row_11_17_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/d11/gcd__of__n__numbers_8cpp.html" target="_self">gcd_of_n_numbers.cpp</a></td><td class="desc">This program aims at calculating the GCD of n numbers by division method </td></tr>
<tr id="row_11_18_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d45/gcd__recursive__euclidean_8cpp.html" target="_self">gcd_recursive_euclidean.cpp</a></td><td class="desc">Compute the greatest common denominator of two integers using <em>recursive form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm">Euclidean algorithm</a> </td></tr>
<tr id="row_11_19_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d9d/large__factorial_8cpp.html" target="_self">large_factorial.cpp</a></td><td class="desc">Compute factorial of any arbitratily large number/ </td></tr>
<tr id="row_11_20_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><a href="d4/d86/large__number_8h_source.html"><span class="icondoc"></span></a><a class="el" href="d4/d86/large__number_8h.html" target="_self">large_number.h</a></td><td class="desc">Library to perform arithmatic operations on arbitrarily large numbers </td></tr>
<tr id="row_11_21_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d7a/largest__power_8cpp.html" target="_self">largest_power.cpp</a></td><td class="desc">Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula </td></tr>
<tr id="row_11_22_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d83/lcm__sum_8cpp.html" target="_self">lcm_sum.cpp</a></td><td class="desc">An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) </td></tr>
<tr id="row_11_23_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d21/least__common__multiple_8cpp.html" target="_self">least_common_multiple.cpp</a></td><td class="desc"></td></tr>
<tr id="row_11_24_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d44/magic__number_8cpp.html" target="_self">magic_number.cpp</a></td><td class="desc">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 </td></tr>
<tr id="row_11_25_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d42/miller__rabin_8cpp.html" target="_self">miller_rabin.cpp</a></td><td class="desc"></td></tr>
<tr id="row_11_26_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/d72/modular__division_8cpp.html" target="_self">modular_division.cpp</a></td><td class="desc">An algorithm to divide two numbers under modulo p <a href="https://www.geeksforgeeks.org/modular-division">Modular Division</a> </td></tr>
<tr id="row_11_27_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d6d/modular__exponentiation_8cpp.html" target="_self">modular_exponentiation.cpp</a></td><td class="desc">C++ Program for Modular Exponentiation Iteratively </td></tr>
<tr id="row_11_28_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html" target="_self">modular_inverse_fermat_little_theorem.cpp</a></td><td class="desc">C++ Program to find the modular inverse using <a href="https://en.wikipedia.org/wiki/Fermat%27s_little_theorem">Fermat's Little Theorem</a> </td></tr>
<tr id="row_11_29_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/dbb/n__choose__r_8cpp.html" target="_self">n_choose_r.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Combination">Combinations</a> n choose r function implementation </td></tr>
<tr id="row_11_30_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/dab/ncr__modulo__p_8cpp.html" target="_self">ncr_modulo_p.cpp</a></td><td class="desc">This program aims at calculating <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html">nCr modulo p</a> </td></tr>
<tr id="row_11_31_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html" target="_self">number_of_positive_divisors.cpp</a></td><td class="desc">C++ Program to calculate the number of positive divisors </td></tr>
<tr id="row_11_32_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/def/power__for__huge__numbers_8cpp.html" target="_self">power_for_huge_numbers.cpp</a></td><td class="desc">Compute powers of large numbers </td></tr>
<tr id="row_11_33_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d0d/prime__factorization_8cpp.html" target="_self">prime_factorization.cpp</a></td><td class="desc">Prime factorization of positive integers </td></tr>
<tr id="row_11_34_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d9b/prime__numbers_8cpp.html" target="_self">prime_numbers.cpp</a></td><td class="desc">Get list of prime numbers </td></tr>
<tr id="row_11_35_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html" target="_self">primes_up_to_billion.cpp</a></td><td class="desc">Compute prime numbers upto 1 billion </td></tr>
<tr id="row_11_36_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d08/realtime__stats_8cpp.html" target="_self">realtime_stats.cpp</a></td><td class="desc">Compute statistics for data entered in rreal-time </td></tr>
<tr id="row_11_37_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html" target="_self">sieve_of_eratosthenes.cpp</a></td><td class="desc">Get list of prime numbers using Sieve of Eratosthenes </td></tr>
<tr id="row_11_38_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="da/d24/sqrt__double_8cpp.html" target="_self">sqrt_double.cpp</a></td><td class="desc">Calculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using <a href="https://en.wikipedia.org/wiki/Bisection_method">bisection method</a> of root-finding </td></tr>
<tr id="row_11_39_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d47/string__fibonacci_8cpp.html" target="_self">string_fibonacci.cpp</a></td><td class="desc">This Programme returns the Nth fibonacci as a string </td></tr>
<tr id="row_11_40_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9d/sum__of__binomial__coefficient_8cpp.html" target="_self">sum_of_binomial_coefficient.cpp</a></td><td class="desc">Algorithm to find sum of binomial coefficients of a given positive integer </td></tr>
<tr id="row_11_41_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d83/sum__of__digits_8cpp.html" target="_self">sum_of_digits.cpp</a></td><td class="desc">A C++ Program to find the Sum of Digits of input integer </td></tr>
<tr id="row_12_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_12_" class="arrow" onclick="toggleFolder('12_')">&#9658;</span><span id="img_12_" class="iconfclosed" onclick="toggleFolder('12_')">&#160;</span><a class="el" href="dir_9c6faab82c22511b50177aa2e38e2780.html" target="_self">numerical_methods</a></td><td class="desc"></td></tr>
<tr id="row_12_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d7/d6a/bisection__method_8cpp.html" target="_self">bisection_method.cpp</a></td><td class="desc">Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Bisection_method">bisection method</a> </td></tr>
<tr id="row_12_1_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d01/brent__method__extrema_8cpp.html" target="_self">brent_method_extrema.cpp</a></td><td class="desc">Find real extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Brent%27s_method">Brent's method</a> </td></tr>
@@ -277,20 +278,21 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
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