In mathematics, a rational number is any number that can be expressed in the form of a fraction p/q , where p & q are two integers, and the denominator q is not equal to zero. Hence, all integers are rational numbers  where denominator, in the most reduced form, is equal to 1.You are given a list of N rational number, {a1/b1, a2/b2, ..., aN/bN}. Print the sum ( = a1/b1 + a2/b2 + ... + aN/bN = num/den) in the most reduced form.InputThe first line of input contains an integer, N, the number of rational numbers.  N lines follow. ithline contains two space separated integers, ai bi, where aiis the numerator and bi is the denominator for the ith rational number.OutputYou have to print two space separated integers, num den, where num and den are numerator and denominator of the sum respectively.Constraints1 <= N <= 151 <= ai <= 101 <= bi <= 10NotesMake sure the sum displayed as output is in the most reduced form.If sum is an integer, you have to print 1 as denominator.Sample Input44 22 42 42 3Sample Output11 3ExplanationSum is 4/2 + 2/4 + 2/4 + 2/3 = (24 + 6 + 6 + 8)/12 = 44/12 = 11/3. So you have to print "11 3", which is the most reduced form.

  1 /*************************************************************************  2  *  Compilation:  javac Rational.java  3  *  Execution:    java Rational  4  *  5  *  Immutable ADT for Rational numbers.   6  *   7  *  Invariants  8  *  -----------  9  *   - gcd(num, den) = 1, i.e, the rational number is in reduced form 10  *   - den >= 1, the denominator is always a positive integer 11  *   - 0/1 is the unique representation of 0 12  * 13  *  We employ some tricks to stave of overflow, but if you 14  *  need arbitrary precision rationals, use BigRational.java. 15  * 16  *************************************************************************/ 17  18 public class Rational implements Comparable<Rational> { 19     private static Rational zero = new Rational(0, 1); 20  21     private int num;   // the numerator 22     private int den;   // the denominator 23  24     // create and initialize a new Rational object 25     public Rational(int numerator, int denominator) { 26  27         // deal with x/0 28         //if (denominator == 0) { 29         //   throw new RuntimeException("Denominator is zero"); 30         //} 31  32         // reduce fraction 33         int g = gcd(numerator, denominator); 34         num = numerator   / g; 35         den = denominator / g; 36  37         // only needed for negative numbers 38         if (den < 0) { den = -den; num = -num; } 39     } 40  41     // return the numerator and denominator of (this) 42     public int numerator()   { return num; } 43     public int denominator() { return den; } 44  45     // return double precision representation of (this) 46     public double toDouble() { 47         return (double) num / den; 48     } 49  50     // return string representation of (this) 51     public String toString() {  52         if (den == 1) return num + ""; 53         else          return num + "/" + den; 54     } 55  56     // return { -1, 0, +1 } if a < b, a = b, or a > b 57     public int compareTo(Rational b) { 58         Rational a = this; 59         int lhs = a.num * b.den; 60         int rhs = a.den * b.num; 61         if (lhs < rhs) return -1; 62         if (lhs > rhs) return +1; 63         return 0; 64     } 65  66     // is this Rational object equal to y? 67     public boolean equals(Object y) { 68         if (y == null) return false; 69         if (y.getClass() != this.getClass()) return false; 70         Rational b = (Rational) y; 71         return compareTo(b) == 0; 72     } 73  74     // hashCode consistent with equals() and compareTo() 75     public int hashCode() { 76         return this.toString().hashCode(); 77     } 78  79  80     // create and return a new rational (r.num + s.num) / (r.den + s.den) 81     public static Rational mediant(Rational r, Rational s) { 82         return new Rational(r.num + s.num, r.den + s.den); 83     } 84  85     // return gcd(|m|, |n|) 86     private static int gcd(int m, int n) { 87         if (m < 0) m = -m; 88         if (n < 0) n = -n; 89         if (0 == n) return m; 90         else return gcd(n, m % n); 91     } 92  93     // return lcm(|m|, |n|) 94     private static int lcm(int m, int n) { 95         if (m < 0) m = -m; 96         if (n < 0) n = -n; 97         return m * (n / gcd(m, n));    // parentheses important to avoid overflow 98     } 99 100     // return a * b, staving off overflow as much as possible by cross-cancellation101     public Rational times(Rational b) {102         Rational a = this;103 104         // reduce p1/q2 and p2/q1, then multiply, where a = p1/q1 and b = p2/q2105         Rational c = new Rational(a.num, b.den);106         Rational d = new Rational(b.num, a.den);107         return new Rational(c.num * d.num, c.den * d.den);108     }109 110 111     // return a + b, staving off overflow112     public Rational plus(Rational b) {113         Rational a = this;114 115         // special cases116         if (a.compareTo(zero) == 0) return b;117         if (b.compareTo(zero) == 0) return a;118 119         // Find gcd of numerators and denominators120         int f = gcd(a.num, b.num);121         int g = gcd(a.den, b.den);122 123         // add cross-product terms for numerator124         Rational s = new Rational((a.num / f) * (b.den / g) + (b.num / f) * (a.den / g),125                                   lcm(a.den, b.den));126 127         // multiply back in128         s.num *= f;129         return s;130     }131 132     // return -a133     public Rational negate() {134         return new Rational(-num, den);135     }136 137     // return a - b138     public Rational minus(Rational b) {139         Rational a = this;140         return a.plus(b.negate());141     }142 143 144     public Rational reciprocal() { return new Rational(den, num);  }145 146     // return a / b147     public Rational divides(Rational b) {148         Rational a = this;149         return a.times(b.reciprocal());150     }151 152 153     // test client154     public static void main(String[] args) {155         Rational x, y, z;156 157         // 1/2 + 1/3 = 5/6158         x = new Rational(1, 2);159         y = new Rational(1, 3);160         z = x.plus(y);161         System.out.println(z);162 163         // 8/9 + 1/9 = 1164         x = new Rational(8, 9);165         y = new Rational(1, 9);166         z = x.plus(y);167         System.out.println(z);168 169         // 1/200000000 + 1/300000000 = 1/120000000170         x = new Rational(1, 200000000);171         y = new Rational(1, 300000000);172         z = x.plus(y);173         System.out.println(z);174 175         // 1073741789/20 + 1073741789/30 = 1073741789/12176         x = new Rational(1073741789, 20);177         y = new Rational(1073741789, 30);178         z = x.plus(y);179         System.out.println(z);180 181         //  4/17 * 17/4 = 1182         x = new Rational(4, 17);183         y = new Rational(17, 4);184         z = x.times(y);185         System.out.println(z);186 187         // 3037141/3247033 * 3037547/3246599 = 841/961 188         x = new Rational(3037141, 3247033);189         y = new Rational(3037547, 3246599);190         z = x.times(y);191         System.out.println(z);192 193         // 1/6 - -4/-8 = -1/3194         x = new Rational( 1,  6);195         y = new Rational(-4, -8);196         z = x.minus(y);197         System.out.println(z);198     }199 200 }