Problem:
Score : 300 points

Problem Statement

AtCoDeer the deer is seeing a quick report of election results on TV.
Two candidates are standing for the election: Takahashi and Aoki.
The report shows the ratio of the current numbers of votes the two candidates have obtained, but not the actual numbers of votes.
AtCoDeer has checked the report N times, and when he checked it for the i-th (1≦i≦N) time, the ratio was T_i:A_i.
It is known that each candidate had at least one vote when he checked the report for the first time.

Find the minimum possible total number of votes obtained by the two candidates when he checked the report for the N-th time.
It can be assumed that the number of votes obtained by each candidate never decreases.

Constraints

1≦N≦1000

1≦T_i,A_i≦1000 (1≦i≦N)

T_i and A_i (1≦i≦N) are coprime.

It is guaranteed that the correct answer is at most 10^{18}.

Input

The input is given from Standard Input in the following format:

N
T_1 A_1
T_2 A_2
:
T_N A_N

Output

Print the minimum possible total number of votes obtained by Takahashi and Aoki when AtCoDeer checked the report for the N-th time.

Sample Input 1

3
2 3
1 1
3 2

Sample Output 1

10

When the numbers of votes obtained by the two candidates change as 2,3 → 3,3 → 6,4, the total number of votes at the end is 10, which is the minimum possible number.

Sample Input 2

4
1 1
1 1
1 5
1 100

Sample Output 2

101

It is possible that neither candidate obtained a vote between the moment when he checked the report, and the moment when he checked it for the next time.

Sample Input 3

5
3 10
48 17
31 199
231 23
3 2

Sample Output 3

6930

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.*
import java.lang.*
import java.util.*

// Constant
val sc = FastScanner()
val pw = PrintWriter(System.out)
const val MOD = 1000000007L
const val INF = 9223372036854775807L

// Main
fun main(args: Array<String>) {
    solve()
    pw.flush()
}

fun solve() {
    val n = nextLong()
    var takahashi = nextLong()
    var aoki = nextLong()

    for (i in 1 until n){
        val t = nextLong()
        val a = nextLong()
        var tNow = takahashi
        var aNow = aoki
        if(t < a){
            val jump = (tNow + t - 1) / t
            tNow = t * jump
            aNow = a * jump
            if(aNow < aoki){
                val jump2 = (aoki + a - 1) / a
                aNow = a * jump2
                tNow = t * jump2
            }
        } else {
            val jump = (aNow + a - 1) / a
            aNow = a * jump
            tNow = t * jump
            if(tNow < takahashi){
                val jump2 = (takahashi + t - 1) / t
                tNow = t * jump2
                aNow = a * jump2
            }
        }

        takahashi = tNow
        aoki = aNow
    }

    println(takahashi + aoki)

}



// Rule
operator fun String.get(index: Long): Char {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun CharArray.get(index: Long): Char {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun CharArray.set(index: Long, value: Char) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}
operator fun LongArray.get(index: Long): Long {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun LongArray.set(index: Long, value: Long) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}
operator fun DoubleArray.get(index: Long): Double {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun DoubleArray.set(index: Long, value: Double) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}
operator fun <T> Array<T>.get(index: Long): T {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun <T> Array<T>.set(index: Long, value: T) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}
operator fun <T> MutableList<T>.get(index: Long): T {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun <T> MutableList<T>.set(index: Long, value: T) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}

val LongArray.siz: Long
    get() = size.toLong()
val <T> Array<T>.siz: Long
    get() = size.toLong()
val <T> MutableList<T>.siz: Long
    get() = size.toLong()
val <T> MutableSet<T>.siz: Long
    get() = size.toLong()
val String.len: Long
    get() = length.toLong()

// Output
fun println(v: String) {
    pw.println(v)
}
fun print(v: String) {
    pw.print(v)
}

// Input
fun next() = sc.next()
fun nextLong() = sc.nextLong()
fun nextDouble() = next().toDouble()
fun nextAry(n: Long): Array<String> {
    val ary = ary(n)
    for (i in 0 until n) ary[i] = next()
    return ary
}
fun nextLongAry(n: Long): LongArray {
    val ary = longAry(n)
    for (i in 0 until n) ary[i] = nextLong()
    return ary
}
fun nextDoubleAry(n: Long): DoubleArray {
    val ary = doubleAry(n)
    for (i in 0 until n) ary[i] = nextDouble()
    return ary
}

// Statement
fun ary(n: Long, init: String = "") = Array(n.toInt()) { init }
fun longAry(n: Long, init: Long = 0L) = LongArray(n.toInt()) { init }
fun doubleAry(n: Long, init: Double = 0.0) = DoubleArray(n.toInt()) { init }
fun boolAry(n: Long, init: Boolean = false) = Array(n.toInt()) { init }
fun ary2(n: Long, m: Long, init: String = "") = Array(n.toInt()) { ary(m, init) }
fun longAry2(n: Long, m: Long, init: Long = 0) = Array(n.toInt()) { longAry(m, init) }
fun doubleAry2(n: Long, m: Long, init: Double = 0.0) = Array(n.toInt()) { doubleAry(m, init) }
fun boolAry2(n: Long, m: Long, init: Boolean = false) = Array(n.toInt()) { boolAry(m, init) }
fun ary3(n: Long, m: Long, k: Long, init: String = "") = Array(n.toInt()) { ary2(m, k, init) }
fun longAry3(n: Long, m: Long, k: Long, init: Long = 0L) = Array(n.toInt()) { longAry2(m, k, init) }
fun doubleAry3(n: Long, m: Long, k: Long, init: Double = 0.0) = Array(n.toInt()) { doubleAry2(m, k, init) }
fun boolAry3(n: Long, m: Long, k: Long, init: Boolean = false) = Array(n.toInt()) { boolAry2(m, k, init) }
fun list() = mutableListOf<String>()
fun longList() = mutableListOf<Long>()
fun doubleList() = mutableListOf<Double>()
fun strSet() = mutableSetOf<String>()
fun longSet() = mutableSetOf<Long>()
fun doubleSet() = mutableSetOf<Double>()
fun <E, V> map() = mutableMapOf<E, V>()

// Monoid
val addFunc = {a: Long, b: Long -> a + b}
val mulFunc = {a: Long, b: Long -> a * b}
val maxFunc = {a: Long, b: Long -> max(a, b)}
val minFunc = {a: Long, b: Long -> min(a, b)}
val gcdFunc = {a: Long, b: Long -> gcd(a, b)}
val lcmFunc = {a: Long, b: Long -> lcm(a, b)}
val xorFunc = {a: Long, b: Long -> a xor b}
fun calc(a: Long, b: Long, op: (Long, Long) -> Long) = op(a, b)

// Extension
fun LongArray.lowerBound(n: Long): Long {
    var ok = this.size.toLong()
    var ng = -1L
    while (abs(ok - ng) > 1) {
        val mid = (ok + ng) / 2
        if (this[mid] >= n) ok = mid
        else ng = mid
    }
    return ok
}
fun DoubleArray.lowerBound(n: Double): Long {
    var ok = this.size.toLong()
    var ng = -1L
    while (abs(ok - ng) > 1) {
        val mid = (ok + ng) / 2
        if (this[mid] >= n) ok = mid
        else ng = mid
    }
    return ok
}
fun MutableList<Long>.longLowerBound(n: Long): Long {
    var ok = this.size.toLong()
    var ng = -1L
    while (abs(ok - ng) > 1) {
        val mid = (ok + ng) / 2
        if (this[mid] >= n) ok = mid
        else ng = mid
    }
    return ok
}
fun MutableList<Double>.doubleLowerBound(n: Double): Long {
    var ok = this.size.toLong()
    var ng = -1L
    while (abs(ok - ng) > 1) {
        val mid = (ok + ng) / 2
        if (this[mid] >= n) ok = mid
        else ng = mid
    }
    return ok
}
fun LongArray.cumsum(op: (Long, Long) -> Long): LongArray {
    val s = longAry(this.size + 1L)
    s[1] = this[0]
    for (i in 1 until this.size) s[i + 1] = calc(s[i], this[i], op)
    return s
}
fun MutableMap<String, Int>.counting(n: Long) {
    repeat(n.toInt()) {
        val a = next()
        if (this.containsKey(a)) this[a] = this[a]!! + 1
        else this[a] = 1
    }
}
fun MutableMap<Long, Int>.longCounting(n: Long) {
    repeat(n.toInt()) {
        val a = nextLong()
        if (this.containsKey(a)) this[a] = this[a]!! + 1
        else this[a] = 1
    }
}

// Mathematics
fun abs(n: Long): Long = Math.abs(n)
fun abs(n: Double): Double = Math.abs(n)
fun max(vararg values: Long) = if (values.isEmpty()) -INF else values.max()!!
fun min(vararg values: Long) = if (values.isEmpty()) INF else values.min()!!
tailrec fun gcd(a: Long, b: Long): Long = if (b == 0L) a else if (a % b == 0L) b else gcd(b, (a % b))
fun lcm(a: Long, b: Long): Long = a / gcd(a, b) * b
fun modpow(a: Long, n: Long, p: Long = MOD): Long {
    var res = 1L
    var ar = a
    var nr = n
    while (nr > 0) {
        if ((nr and 1) == 1L) res = res * ar % p
        ar = ar * ar % p
        nr = nr shr 1
    }
    return res
}
fun modinv(a: Long, p: Long = MOD): Long = modpow(a, p - 2, p)
fun ncr(n: Long, r: Long): Long {
    var a = 1L
    var b = 1L
    for (i in 1..r) {
        a = a * (n + 1 - i) % MOD
        b = b * i % MOD
    }
    return modinv(b, MOD) * a % MOD
}

class Combination(private val max: Long) {
    private val fac = longAry(max)
    private val finv = longAry(max)
    private val inv = longAry(max)
    private val p = MOD
    fun init() {
        fac[0] = 1
        fac[1] = 1
        finv[0] = 1
        finv[1] = 1
        inv[1] = 1
        for (i in 2 until max) {
            fac[i] = fac[i - 1] * i % p
            inv[i] = p - inv[p % i] * (p / i) % p;
            finv[i] = finv[i - 1] * inv[i] % p
        }
    }

    fun com(n: Long, r: Long): Long = if (n < r || (n < 0 || r < 0)) 0L else fac[n] * (finv[r] * finv[n - r] % p) % p
}

class Permutation(private val n: Long, private var searched: Long = 0L, private var nextIndex: Long = 0L) {
    private val size = fact(n)
    private val permList = longAry2(size, n)

    private tailrec fun fact(n: Long, ans: Long = 1L): Long {
        return if (n == 0L) ans
        else fact(n - 1, ans * n)
    }

    fun init() {
        create(0, longAry(n), boolAry(n))
    }

    private fun create(num: Long, list: LongArray, flag: Array<Boolean>) {
        if (num == n) {
            permList[searched] = list.copyOf()
            searched++
        }
        for (i in 0 until n) {
            if (flag[i]) continue
            list[num] = i
            flag[i] = true
            create(num + 1, list, flag)
            flag[i] = false
        }
    }

    fun hasNext(): Boolean {
        return if (nextIndex < size) {
            true
        } else {
            nextIndex = 0
            false
        }
    }

    fun nextPerm(): LongArray = permList[nextIndex++]
}

// Graph
data class Node(val id: Long, var past: Long = -1, val edges: MutableList<Edge> = mutableListOf())
data class Edge(val from: Long, val to: Long, val cost: Long = 1L)

fun dfs(nodes: Array<Node>, now: Long, seen: Array<Boolean>) {
    seen[now] = true
    for (edge in nodes[now].edges) {
        if (seen[edge.to]) continue
        dfs(nodes, edge.to, seen)
    }
}

fun bfs(nodes: Array<Node>, start: Long): LongArray {
    val queue = ArrayDeque<Long>()
    queue.add(start)
    val dist = longAry(nodes.size.toLong(), -1L)
    dist[start] = 0L
    while (queue.isNotEmpty()) {
        val now = queue.poll()
        for (edge in nodes[now].edges) {
            if (dist[edge.to] != -1L) continue
            dist[edge.to] = dist[now] + 1
            queue.add(edge.to)
        }
    }
    return dist
}

fun dijkstra(nodes: Array<Node>, start: Long): LongArray {
    val queue = PriorityQueue(16) { e1: Edge, e2: Edge ->
        return@PriorityQueue when {
            e1.cost < e2.cost -> -1
            e2.cost > e1.cost -> 1
            else -> 0
        }
    }
    queue.add(Edge(start, start, 0L))
    val dist = longAry(nodes.size.toLong(), INF / 2)
    dist[start] = 0
    while (queue.isNotEmpty()) {
        val now = queue.poll()
        if (dist[now.to] < now.cost) continue;
        for (edge in nodes[now.to].edges) {
            if (dist[edge.to] <= dist[edge.from] + edge.cost) continue
            dist[edge.to] = dist[edge.from] + edge.cost
            queue.add(Edge(edge.from, edge.to, dist[edge.to]))
            nodes[edge.to].past = edge.from
        }
    }
    return dist
}

// Data Structure
class UnionFind(size: Long) {
    private val par = LongArray(size.toInt()) { it.toLong() }
    private val size = longAry(size, 1L)
    fun root(x: Long): Long {
        return if (par[x] == x) {
            x
        } else {
            par[x] = root(par[x])
            par[x]
        }
    }

    fun same(x: Long, y: Long): Boolean = root(x) == root(y)
    fun unite(x: Long, y: Long) {
        var a = root(x)
        var b = root(y)
        if (a == b) return
        if (size[a] < size[b]) {
            var tmp = a
            a = b
            b = tmp
        }
        size[a] += size[b]
        par[b] = a
    }

    fun size(x: Long): Long = size[root(x)]
}

class SegmentTree(
    private val a: LongArray,
    private val op: (Long, Long) -> Long,
    private val def: Long = 0,
    private val size: Int = a.size,
    private val n: Int = Integer.highestOneBit(size) shl 1
) {
    private val nodes = longAry(2L * n - 1, def)

    fun init() {
        for (i in 0 until size) nodes[i + n - 1] = a[i]
        for (i in n - 2 downTo 0) nodes[i] = calc(nodes[2 * i + 1], nodes[2 * i + 2], op)
    }

    fun update(x: Long, value: Long) {
        var index = x + n - 1
        nodes[index] = value
        while (index > 0) {
            index = (index - 1) / 2
            nodes[index] = calc(nodes[2 * index + 1], nodes[2 * index + 2], op)
        }
    }

    fun get(a: Long, b: Long) = getSub(a, b, 0L, 0L, n.toLong())
    private fun getSub(a: Long, b: Long, k: Long, l: Long, r: Long): Long {
        return when {
            r <= a || b <= l -> def
            a <= l && r <= b -> nodes[k]
            else -> {
                val vl = getSub(a, b, k * 2 + 1, l, (l + r) / 2)
                val vr = getSub(a, b, k * 2 + 2, (l + r) / 2, r)
                calc(vl, vr, op)
            }
        }
    }

    fun joinToString(separator: String) = nodes.drop(n - 1).take(size).joinToString(separator)
}

// Scanner
class FastScanner {
    private val sin: InputStream = System.`in`
    private val buffer: ByteArray = ByteArray(1024) { 0 }
    private var ptr = 0
    private var buflen = 0

    private fun hasNextByte(): Boolean {
        return when {
            ptr < buflen -> true
            else -> {
                ptr = 0
                buflen = sin.read(buffer)
                if (buflen <= 0) false
                true
            }
        }
    }

    private fun readByte(): Int {
        return when {
            hasNextByte() -> buffer[ptr++].toInt()
            else -> -1
        }
    }

    private fun isPrintableChar(c: Int) = c in 33..126

    fun hasNext(): Boolean {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
        return hasNextByte()
    }

    fun next(): String {
        if (!hasNext()) throw NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b)
            b = readByte()
        }
        return sb.toString()
    }

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0L
        var minus = false
        var b = readByte()
        if (b.toChar() == '-') {
            minus = true
            b = readByte()
        }
        if (b.toChar() !in '0'..'9') throw NumberFormatException()
        while (true) {
            when {
                b.toChar() in '0'..'9' -> {
                    n *= 10
                    n += b.toChar() - '0'
                }
                b == -1 || !isPrintableChar(b) -> return if (minus) -n else n
                else -> throw NumberFormatException()
            }
            b = readByte()
        }
    }

//    "The world doesn't need you."
//
//    fun nextInt(): Int {
//        val nl = nextLong()
//        if (nl !in Int.MIN_VALUE..Int.MAX_VALUE) throw NumberFormatException()
//        return nl.toInt()
//    }
}