import java.util.*
import kotlin.*

import java.io.InputStream
import java.lang.NumberFormatException
import java.lang.StringBuilder


fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = FastScanner()
        val n = sc.nextInt()
        val t = Array(n) { sc.nextInt() }
        val tSum = t.sum()
        val v = Array(n) { sc.nextInt() }
        val dp = Array(tSum + 1) { Array(101) { Double.MIN_VALUE } }
        val flag = Array(tSum + 1) { Array(101) { false } }
        dp[0][0] = 0.0
        flag[0][0] = true
        var index = 0
        var cnt = 0
        for (i in 0 until tSum) {
            for (j in 0..100) {
                if (!flag[i][j]) continue

                if (j + 1 <= v[index]) {
                    dp[i + 1][j + 1] = Math.max(dp[i + 1][j + 1], dp[i][j] + j + 0.5)
                    flag[i + 1][j + 1] = true
                }
                if (j - 1 >= 0 && j <= v[index]) {
                    dp[i + 1][j - 1] = Math.max(dp[i + 1][j - 1], dp[i][j] + j - 0.5)
                    flag[i + 1][j - 1] = true
                }
                if (j <= v[index]) {
                    dp[i + 1][j] = Math.max(dp[i + 1][j], dp[i][j] + j + if (j < v[index]) 0.25 else 0.0)
                    flag[i + 1][j] = true
                }
            }
            cnt++
            if (cnt >= t[index]) {
                index++
                cnt = 0
            }
        }
        println(dp[tSum][0])
    }
}


class FastScanner {
    companion object {
        val input: InputStream = System.`in`
        val buffer = ByteArray(1024) { 0 }
        fun isPrintableChar(c: Int): Boolean = c in 33..126
    }

    var ptr = 0
    var buflen = 0
    private fun hasNextByte(): Boolean {
        if (ptr < buflen) {
            return true
        } else {
            ptr = 0
            buflen = input.read(buffer)
            if (buflen <= 0) {
                return false
            }
        }
        return true
    }

    private fun readByte(): Int = if (hasNextByte()) buffer[ptr++].toInt() else -1

    private fun skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
    }

    fun hasNext(): Boolean {
        skipUnprintable()
        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 nextInt(): Int {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0L
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextDouble(): Double = next().toDouble()
}


Measured memory_bytes: 133760