Shakespeare is a widely known esoteric programming language in which programs look like plays by Shakespeare, and numbers are given by combinations of ornate epithets. In this problem we will have a closer look at the way the numbers are described in Shakespeare.

Each constant in Shakespeare is created from non-negative powers of 2 using arithmetic operations. For simplicity we'll allow only addition and subtraction and will look for a representation of the given number which requires a minimal number of operations.

You are given an integer *n*. You have to represent it as *n* = *a*<sub class="lower-index">1</sub> + *a*<sub class="lower-index">2</sub> + ... + *a*<sub class="lower-index">*m*</sub>, where each of *a*<sub class="lower-index">*i*</sub> is a non-negative power of 2, possibly multiplied by -1. Find a representation which minimizes the value of *m*.
The only line of input contains a positive integer *n*, written as its binary notation. The length of the notation is at most 10<sup class="upper-index">6</sup>. The first digit of the notation is guaranteed to be 1.
1111
2
+2^4
-2^0
1010011
4
+2^0
+2^1
+2^4
+2^6
1
1
+2^0
10110111
4
+2^8
-2^6
-2^3
-2^0
10101110
4
+2^8
-2^6
-2^4
-2^1
1011001
4
+2^0
+2^3
+2^4
+2^6
10001
2
+2^0
+2^4
10
1
+2^1
11
2
+2^0
+2^1
100
1
+2^2
100
1
+2^2
111
2
+2^3
-2^0
1000000000
1
+2^9
1011000000
3
+2^6
+2^7
+2^9
1100010000
3
+2^4
+2^8
+2^9
1000111001
4
+2^0
+2^6
-2^3
+2^9
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1
+2^99
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1
+2^99
1000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000
2
+2^18
+2^99
1000000000000000000000000000010000000000000000100000000000100000000000000000000000000000000000000000
4
+2^41
+2^53
+2^70
+2^99
1000000000000000000100000001000000000000000000100000101000000000000000000000100000000000000100000000
8
+2^8
+2^23
+2^45
+2^47
+2^53
+2^72
+2^80
+2^99
1000100000101000000100100000000000000000100000000000000010000010000001010010100000000000000001001000
15
+2^3
+2^6
+2^23
+2^25
+2^28
+2^30
+2^37
+2^43
+2^59
+2^77
+2^80
+2^87
+2^89
+2^95
+2^99
1000001001000011000010001000100110010110100000000101010101000100100010000100000100000100001000000000
26
+2^9
+2^14
+2^20
+2^26
+2^31
+2^35
+2^38
+2^42
+2^44
+2^46
+2^48
+2^50
+2^59
+2^61
+2^62
+2^64
+2^67
+2^68
+2^71
+2^75
+2^79
+2^84
+2^85
+2^90
+2^93
+2^99
1110000000001011100111001010000010101100010101001101001010101100011101100110000010000101110101000011
37
+2^0
+2^1
+2^6
+2^8
+2^15
-2^13
-2^10
+2^19
+2^25
+2^26
+2^35
-2^31
-2^29
+2^38
+2^39
+2^41
+2^43
+2^45
+2^48
+2^50
+2^51
+2^54
+2^56
+2^58
+2^62
+2^63
+2^65
+2^67
+2^73
+2^75
+2^81
-2^78
+2^88
-2^86
-2^83
+2^100
-2^97
1001110101111100101111011111111111101010111111010111011111111111011111111111111100011011111111111101
20
+2^0
+2^17
-2^14
-2^2
+2^84
-2^82
-2^77
-2^64
-2^62
-2^60
-2^53
-2^51
-2^47
-2^35
-2^20
+2^97
-2^93
-2^91
-2^86
+2^99
1111111101111111101111111111101111111111111111111111101111111011111110011111101111111110111111111111
11
+2^29
-2^22
-2^12
-2^0
+2^100
-2^91
-2^82
-2^70
-2^46
-2^38
-2^31
100000000000000000000000000000000
1
+2^32
111111000111111000111111000111111
8
+2^6
-2^0
+2^15
-2^9
+2^24
-2^18
+2^33
-2^27
10001100000000000011011011
7
+2^8
-2^5
-2^2
-2^0
+2^20
+2^21
+2^25
1101011
4
+2^7
-2^4
-2^2
-2^0
11000101010000101101101101111000100100001101001111000011011100
21
+2^8
-2^5
-2^2
+2^16
-2^12
+2^18
+2^20
+2^21
+2^26
+2^29
+2^48
-2^46
-2^43
-2^40
-2^37
-2^33
+2^52
+2^54
+2^56
+2^60
+2^61
11101011
4
+2^8
-2^4
-2^2
-2^0
print("_RANDOM_GUESS_1692122417.3541136")# 1692122417.3541307