package main

import (
	"bufio"
	"errors"
	"fmt"
	"io"
	"math"
	"os"
	"strconv"
)

/*********** I/O ***********/

var (
	// ReadString returns a WORD string.
	ReadString func() string
	stdout     *bufio.Writer
)

func init() {
	ReadString = newReadString(os.Stdin)
	stdout = bufio.NewWriter(os.Stdout)
}

func newReadString(ior io.Reader) func() string {
	r := bufio.NewScanner(ior)
	// r.Buffer(make([]byte, 1024), int(1e+11)) // for AtCoder
	r.Buffer(make([]byte, 1024), int(1e+9)) // for Codeforces
	// Split sets the split function for the Scanner. The default split function is ScanLines.
	// Split panics if it is called after scanning has started.
	r.Split(bufio.ScanWords)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

// ReadInt returns an integer.
func ReadInt() int {
	return int(readInt64())
}
func ReadInt2() (int, int) {
	return int(readInt64()), int(readInt64())
}
func ReadInt3() (int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64())
}
func ReadInt4() (int, int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64()), int(readInt64())
}

// ReadInt64 returns as integer as int64.
func ReadInt64() int64 {
	return readInt64()
}
func ReadInt64_2() (int64, int64) {
	return readInt64(), readInt64()
}
func ReadInt64_3() (int64, int64, int64) {
	return readInt64(), readInt64(), readInt64()
}
func ReadInt64_4() (int64, int64, int64, int64) {
	return readInt64(), readInt64(), readInt64(), readInt64()
}

func readInt64() int64 {
	i, err := strconv.ParseInt(ReadString(), 0, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// ReadIntSlice returns an integer slice that has n integers.
func ReadIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt()
	}
	return b
}

// ReadInt64Slice returns as int64 slice that has n integers.
func ReadInt64Slice(n int) []int64 {
	b := make([]int64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt64()
	}
	return b
}

// ReadFloat64 returns an float64.
func ReadFloat64() float64 {
	return float64(readFloat64())
}

func readFloat64() float64 {
	f, err := strconv.ParseFloat(ReadString(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// ReadFloatSlice returns an float64 slice that has n float64.
func ReadFloat64Slice(n int) []float64 {
	b := make([]float64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadFloat64()
	}
	return b
}

// ReadRuneSlice returns a rune slice.
func ReadRuneSlice() []rune {
	return []rune(ReadString())
}

/*********** Debugging ***********/

// ZeroPaddingRuneSlice returns binary expressions of integer n with zero padding.
// For debugging use.
func ZeroPaddingRuneSlice(n, digitsNum int) []rune {
	sn := fmt.Sprintf("%b", n)

	residualLength := digitsNum - len(sn)
	if residualLength <= 0 {
		return []rune(sn)
	}

	zeros := make([]rune, residualLength)
	for i := 0; i < len(zeros); i++ {
		zeros[i] = '0'
	}

	res := []rune{}
	res = append(res, zeros...)
	res = append(res, []rune(sn)...)

	return res
}

// Strtoi is a wrapper of strconv.Atoi().
// If strconv.Atoi() returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

// PrintIntsLine returns integers string delimited by a space.
func PrintIntsLine(A ...int) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.Itoa(A[i])
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintIntsLine returns integers string delimited by a space.
func PrintInts64Line(A ...int64) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.FormatInt(A[i], 10) // 64bit int version
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintDebug is wrapper of fmt.Fprintf(os.Stderr, format, a...)
func PrintDebug(format string, a ...interface{}) {
	fmt.Fprintf(os.Stderr, format, a...)
}

/********** FAU standard libraries **********/

//fmt.Sprintf("%b\n", 255) 	// binary expression

/********** I/O usage **********/

//str := ReadString()
//i := ReadInt()
//X := ReadIntSlice(n)
//S := ReadRuneSlice()
//a := ReadFloat64()
//A := ReadFloat64Slice(n)

//str := ZeroPaddingRuneSlice(num, 32)
//str := PrintIntsLine(X...)

/*
ASCII code

ASCII   10進数  ASCII   10進数  ASCII   10進数
!       33      "       34      #       35
$       36      %       37      &       38
'       39      (       40      )       41
*       42      +       43      ,       44
-       45      .       46      /       47
0       48      1       49      2       50
3       51      4       52      5       53
6       54      7       55      8       56
9       57      :       58      ;       59
<       60      =       61      >       62
?       63      @       64      A       65
B       66      C       67      D       68
E       69      F       70      G       71
H       72      I       73      J       74
K       75      L       76      M       77
N       78      O       79      P       80
Q       81      R       82      S       83
T       84      U       85      V       86
W       87      X       88      Y       89
Z       90      [       91      \       92
]       93      ^       94      _       95
`       96      a       97      b       98
c       99      d       100     e       101
f       102     g       103     h       104
i       105     j       106     k       107
l       108     m       109     n       110
o       111     p       112     q       113
r       114     s       115     t       116
u       117     v       118     w       119
x       120     y       121     z       122
{       123     |       124     }       125
~       126             127
*/

/*******************************************************************/

const (
	// General purpose
	MOD          = 1000000000 + 7
	ALPHABET_NUM = 26
	INF_INT64    = math.MaxInt64
	INF_BIT60    = 1 << 60
	INF_INT32    = math.MaxInt32
	INF_BIT30    = 1 << 30
	NIL          = -1

	// for dijkstra, prim, and so on
	WHITE = 0
	GRAY  = 1
	BLACK = 2
)

var (
	a, b, m int
	A, B    []int
	X, Y, C []int
)

func main() {
	a, b, m = ReadInt3()
	A = ReadIntSlice(a)
	B = ReadIntSlice(b)
	for i := 0; i < m; i++ {
		x, y, c := ReadInt3()
		x--
		y--
		X = append(X, x)
		Y = append(Y, y)
		C = append(C, c)
	}

	minReizou := Min(A...)
	minRange := Min(B...)

	// ans := INF_BIT60
	ans := minReizou + minRange
	for i := 0; i < m; i++ {
		x, y, c := X[i], Y[i], C[i]

		val := A[x] + B[y] - c
		ChMin(&ans, val)
	}
	fmt.Println(ans)
}

// Min returns the min integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Min(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m > integer {
			m = integer
		}
	}
	return m
}

// ChMin accepts a pointer of integer and a target value.
// If target value is SMALLER than the first argument,
//	then the first argument will be updated by the second argument.
func ChMin(updatedValue *int, target int) bool {
	if *updatedValue > target {
		*updatedValue = target
		return true
	}
	return false
}

/*
- まずは全探索を検討しましょう
- MODは最後にとりましたか？
- 負のMODはちゃんと関数を使って処理していますか？
- ループを抜けた後も処理が必要じゃありませんか？
- 和・積・あまりを求められたらint64が必要ではありませんか？
- いきなりオーバーフローはしていませんか？
- MOD取る系はint64必須ですよ？
- 後ろ・逆・ゴールから考えましたか？
- 3者のうち真ん中に着目しましたか？
*/

/*******************************************************************/


Measured memory_bytes: 11776