1148_A. Another One Bites The Dust_36640
Let's call a string good if and only if it consists of only two types of letters — 'a' and 'b' and every two consecutive letters are distinct. For example "baba" and "aba" are good strings and "abb" is a bad string.

You have a strings "a", b strings "b" and c strings "ab". You want to choose some subset of these strings and concatenate them in any arbitrarily order.

What is the length of the longest good string you can obtain this way?

Input

The first line contains three positive integers a, b, c (1 ≤ a, b, c ≤ 10^9) — the number of strings "a", "b" and "ab" respectively.

Output

Print a single number — the maximum possible length of the good string you can obtain.

Examples

Input


1 1 1


Output


4


Input


2 1 2


Output


7


Input


3 5 2


Output


11


Input


2 2 1


Output


6


Input


1000000000 1000000000 1000000000


Output


4000000000

Note

In the first example the optimal string is "baba".

In the second example the optimal string is "abababa".

In the third example the optimal string is "bababababab".

In the fourth example the optimal string is "ababab".
a,b,c=map(int,input().split())
dif=abs(a-b)
if dif <=1:
    print(a+b+c*2)
else:
    print(min(a,b)*2+1+c*2)
2 2 1
 1 1 1
 2 1 2
 1000000000 1000000000 1000000000
 3 5 2
 1 1 2
 11 9 6
 10 2 5
 6 1 1
 2 100 1
 135266639 299910226 320610730
 100 101 102
 300 1 100
 700 800 1900
 13350712 76770926 61331309
 7 3 4
 6 14 1
 5 2 2
 3 7 5
 6 8 1
 6 1 6
 7 5 12
 1000000000 1000000000 99999999
 894 197 325
 1000 100 10
 7 9 7
 4394826 2233224 609367
 3 4 1
 8 4 5
 2 2 3
 4 8 5
 100 101 99
 17843355 6588793 15517352
 142098087 687355301 987788392
 1 2 1
 3 9 1
 254762 244010 3461323
 3 5 10
 1 1 4
 3 6 3
 8 8 7
 3 1 3
 4 2 6
 1 2 8
 5 5 4
 6 7 1000
 1 5 10
 2 4 1
 3 1 8
 1000000000 1 1
 10 1 1
 4 8 10
 8581 6058 3019
 1 2333 2333
 3698483 6798912 18096063
 333625 453145 800800
 41764 97259 54586
 1 1 3
 13 9 6
 10 2 9
 9 1 1
 197867426 299910226 320610730
 101 101 102
 285 1 100
 504 800 1900
 13350712 114170371 61331309
 7 6 4
 11 14 1
 6 2 2
 1 7 5
 11 8 1
 10 2 1
 7 5 16
 1000000000 1000010000 99999999
 894 175 325
 1000 100 8
 4863867 2233224 609367
 8 8 5
 4 8 4
 100 001 99
 17843355 9688366 15517352
 226308498 687355301 987788392
 254762 137778 3461323
 1 1 0
 5 5 2
 6 7 1010
 4 4 1
 12702 6058 3019
 1 2333 2170
 3698483 2324875 18096063
 372475 453145 800800
 2583 97259 54586
 1 2 0
 1000000000 1010000000 1000000000
 13 9 8
 10 2 11
 197867426 299910226 303341143
 101 001 102
 16230747 114170371 61331309
 2 5 16
 1000000100 1000010000 99999999
 1000 100 14
 4863867 3944839 609367
 17843355 5341099 15517352
 226308498 687355301 1609051733
 3 13 2
 254762 137778 1740862
 1 0 0
 4 4 10
 1 4 6
 6 2 1010
 1 100 1
 7 9 4
 3 4 0
 2 1 3
 1 3 1
 3 13 1
 3 3 10
 3 6 0
 3 8 7
 3 1 2
 4 2 10
 1 4 8
 0 5 10
 5 1 8
 1010000000 1 1
 10 1 2
 4 8 8
 2 2 2
 2 1 0
 1 5 2
 1 0 3
 9 1 0
 1 100 0
 285 0 100
 504 1221 1900
 7 6 2
 11 14 2
 3 2 2
 1 12 5
 11 8 2
 10 2 2
 211 175 325
 7 9 3
 6 4 0
 6 8 5
 1 1 6
 0 8 4
 101 001 99
 2 3 1
 1 3 10
 0 6 0
 3 6 7
 3 1 0
 5 1 2
 -1 5 10
 4 0 1

6
 4
 7
 4000000000
 11
 6
 31
 15
 5
 7
 911754739
 405
 203
 5201
 149364043
 15
 15
 9
 17
 15
 15
 35
 2199999998
 1045
 221
 29
 5685183
 9
 19
 10
 19
 399
 44212291
 2259772959
 5
 9
 7410667
 27
 10
 13
 30
 9
 17
 19
 18
 2013
 23
 7
 19
 5
 5
 29
 18155
 4669
 43589093
 2268851
 192701
 8
 31
 23
 5
 1036956313
 406
 203
 4809
 149364043
 21
 25
 9
 13
 19
 7
 43
 2199999999
 1001
 217
 5685183
 26
 17
 201
 50411437
 2428193781
 7198203
 2
 14
 2033
 10
 18155
 4343
 40841877
 2346551
 114339
 3
 4000000001
 35
 27
 1002417139
 207
 155124113
 37
 2200000199
 229
 9108413
 41716903
 3670720463
 11
 3757281
 1
 28
 15
 2025
 5
 23
 7
 9
 5
 9
 26
 7
 21
 7
 25
 19
 21
 19
 5
 7
 25
 8
 3
 7
 7
 3
 3
 201
 4809
 17
 27
 9
 13
 21
 9
 1001
 21
 9
 23
 14
 9
 201
 7
 23
 1
 21
 3
 7
 19
 3
