zig/lib/std/base64.zig
Andrew Kelley 3fc6fc6812 std.builtin.Endian: make the tags lower case
Let's take this breaking change opportunity to fix the style of this
enum.
2023-10-31 21:37:35 -04:00

546 lines
23 KiB
Zig

const std = @import("std.zig");
const assert = std.debug.assert;
const builtin = @import("builtin");
const testing = std.testing;
const mem = std.mem;
pub const Error = error{
InvalidCharacter,
InvalidPadding,
NoSpaceLeft,
};
const decoderWithIgnoreProto = *const fn (ignore: []const u8) Base64DecoderWithIgnore;
/// Base64 codecs
pub const Codecs = struct {
alphabet_chars: [64]u8,
pad_char: ?u8,
decoderWithIgnore: decoderWithIgnoreProto,
Encoder: Base64Encoder,
Decoder: Base64Decoder,
};
pub const standard_alphabet_chars = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/".*;
fn standardBase64DecoderWithIgnore(ignore: []const u8) Base64DecoderWithIgnore {
return Base64DecoderWithIgnore.init(standard_alphabet_chars, '=', ignore);
}
/// Standard Base64 codecs, with padding
pub const standard = Codecs{
.alphabet_chars = standard_alphabet_chars,
.pad_char = '=',
.decoderWithIgnore = standardBase64DecoderWithIgnore,
.Encoder = Base64Encoder.init(standard_alphabet_chars, '='),
.Decoder = Base64Decoder.init(standard_alphabet_chars, '='),
};
/// Standard Base64 codecs, without padding
pub const standard_no_pad = Codecs{
.alphabet_chars = standard_alphabet_chars,
.pad_char = null,
.decoderWithIgnore = standardBase64DecoderWithIgnore,
.Encoder = Base64Encoder.init(standard_alphabet_chars, null),
.Decoder = Base64Decoder.init(standard_alphabet_chars, null),
};
pub const url_safe_alphabet_chars = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_".*;
fn urlSafeBase64DecoderWithIgnore(ignore: []const u8) Base64DecoderWithIgnore {
return Base64DecoderWithIgnore.init(url_safe_alphabet_chars, null, ignore);
}
/// URL-safe Base64 codecs, with padding
pub const url_safe = Codecs{
.alphabet_chars = url_safe_alphabet_chars,
.pad_char = '=',
.decoderWithIgnore = urlSafeBase64DecoderWithIgnore,
.Encoder = Base64Encoder.init(url_safe_alphabet_chars, '='),
.Decoder = Base64Decoder.init(url_safe_alphabet_chars, '='),
};
/// URL-safe Base64 codecs, without padding
pub const url_safe_no_pad = Codecs{
.alphabet_chars = url_safe_alphabet_chars,
.pad_char = null,
.decoderWithIgnore = urlSafeBase64DecoderWithIgnore,
.Encoder = Base64Encoder.init(url_safe_alphabet_chars, null),
.Decoder = Base64Decoder.init(url_safe_alphabet_chars, null),
};
pub const Base64Encoder = struct {
alphabet_chars: [64]u8,
pad_char: ?u8,
/// A bunch of assertions, then simply pass the data right through.
pub fn init(alphabet_chars: [64]u8, pad_char: ?u8) Base64Encoder {
assert(alphabet_chars.len == 64);
var char_in_alphabet = [_]bool{false} ** 256;
for (alphabet_chars) |c| {
assert(!char_in_alphabet[c]);
assert(pad_char == null or c != pad_char.?);
char_in_alphabet[c] = true;
}
return Base64Encoder{
.alphabet_chars = alphabet_chars,
.pad_char = pad_char,
};
}
/// Compute the encoded length
pub fn calcSize(encoder: *const Base64Encoder, source_len: usize) usize {
if (encoder.pad_char != null) {
return @divTrunc(source_len + 2, 3) * 4;
} else {
const leftover = source_len % 3;
return @divTrunc(source_len, 3) * 4 + @divTrunc(leftover * 4 + 2, 3);
}
}
/// dest.len must at least be what you get from ::calcSize.
pub fn encode(encoder: *const Base64Encoder, dest: []u8, source: []const u8) []const u8 {
const out_len = encoder.calcSize(source.len);
assert(dest.len >= out_len);
var idx: usize = 0;
var out_idx: usize = 0;
while (idx + 15 < source.len) : (idx += 12) {
const bits = std.mem.readInt(u128, source[idx..][0..16], .big);
inline for (0..16) |i| {
dest[out_idx + i] = encoder.alphabet_chars[@truncate((bits >> (122 - i * 6)) & 0x3f)];
}
out_idx += 16;
}
while (idx + 3 < source.len) : (idx += 3) {
const bits = std.mem.readInt(u32, source[idx..][0..4], .big);
dest[out_idx] = encoder.alphabet_chars[(bits >> 26) & 0x3f];
dest[out_idx + 1] = encoder.alphabet_chars[(bits >> 20) & 0x3f];
dest[out_idx + 2] = encoder.alphabet_chars[(bits >> 14) & 0x3f];
dest[out_idx + 3] = encoder.alphabet_chars[(bits >> 8) & 0x3f];
out_idx += 4;
}
if (idx + 2 < source.len) {
dest[out_idx] = encoder.alphabet_chars[source[idx] >> 2];
dest[out_idx + 1] = encoder.alphabet_chars[((source[idx] & 0x3) << 4) | (source[idx + 1] >> 4)];
dest[out_idx + 2] = encoder.alphabet_chars[(source[idx + 1] & 0xf) << 2 | (source[idx + 2] >> 6)];
dest[out_idx + 3] = encoder.alphabet_chars[source[idx + 2] & 0x3f];
out_idx += 4;
} else if (idx + 1 < source.len) {
dest[out_idx] = encoder.alphabet_chars[source[idx] >> 2];
dest[out_idx + 1] = encoder.alphabet_chars[((source[idx] & 0x3) << 4) | (source[idx + 1] >> 4)];
dest[out_idx + 2] = encoder.alphabet_chars[(source[idx + 1] & 0xf) << 2];
out_idx += 3;
} else if (idx < source.len) {
dest[out_idx] = encoder.alphabet_chars[source[idx] >> 2];
dest[out_idx + 1] = encoder.alphabet_chars[(source[idx] & 0x3) << 4];
out_idx += 2;
}
if (encoder.pad_char) |pad_char| {
for (dest[out_idx..out_len]) |*pad| {
pad.* = pad_char;
}
}
return dest[0..out_len];
}
};
pub const Base64Decoder = struct {
const invalid_char: u8 = 0xff;
const invalid_char_tst: u32 = 0xff000000;
/// e.g. 'A' => 0.
/// `invalid_char` for any value not in the 64 alphabet chars.
char_to_index: [256]u8,
fast_char_to_index: [4][256]u32,
pad_char: ?u8,
pub fn init(alphabet_chars: [64]u8, pad_char: ?u8) Base64Decoder {
var result = Base64Decoder{
.char_to_index = [_]u8{invalid_char} ** 256,
.fast_char_to_index = .{[_]u32{invalid_char_tst} ** 256} ** 4,
.pad_char = pad_char,
};
var char_in_alphabet = [_]bool{false} ** 256;
for (alphabet_chars, 0..) |c, i| {
assert(!char_in_alphabet[c]);
assert(pad_char == null or c != pad_char.?);
const ci = @as(u32, @intCast(i));
result.fast_char_to_index[0][c] = ci << 2;
result.fast_char_to_index[1][c] = (ci >> 4) | ((ci & 0x0f) << 12);
result.fast_char_to_index[2][c] = ((ci & 0x3) << 22) | ((ci & 0x3c) << 6);
result.fast_char_to_index[3][c] = ci << 16;
result.char_to_index[c] = @as(u8, @intCast(i));
char_in_alphabet[c] = true;
}
return result;
}
/// Return the maximum possible decoded size for a given input length - The actual length may be less if the input includes padding.
/// `InvalidPadding` is returned if the input length is not valid.
pub fn calcSizeUpperBound(decoder: *const Base64Decoder, source_len: usize) Error!usize {
var result = source_len / 4 * 3;
const leftover = source_len % 4;
if (decoder.pad_char != null) {
if (leftover % 4 != 0) return error.InvalidPadding;
} else {
if (leftover % 4 == 1) return error.InvalidPadding;
result += leftover * 3 / 4;
}
return result;
}
/// Return the exact decoded size for a slice.
/// `InvalidPadding` is returned if the input length is not valid.
pub fn calcSizeForSlice(decoder: *const Base64Decoder, source: []const u8) Error!usize {
const source_len = source.len;
var result = try decoder.calcSizeUpperBound(source_len);
if (decoder.pad_char) |pad_char| {
if (source_len >= 1 and source[source_len - 1] == pad_char) result -= 1;
if (source_len >= 2 and source[source_len - 2] == pad_char) result -= 1;
}
return result;
}
/// dest.len must be what you get from ::calcSize.
/// Invalid characters result in `error.InvalidCharacter`.
/// Invalid padding results in `error.InvalidPadding`.
pub fn decode(decoder: *const Base64Decoder, dest: []u8, source: []const u8) Error!void {
if (decoder.pad_char != null and source.len % 4 != 0) return error.InvalidPadding;
var dest_idx: usize = 0;
var fast_src_idx: usize = 0;
var acc: u12 = 0;
var acc_len: u4 = 0;
var leftover_idx: ?usize = null;
while (fast_src_idx + 16 < source.len and dest_idx + 15 < dest.len) : ({
fast_src_idx += 16;
dest_idx += 12;
}) {
var bits: u128 = 0;
inline for (0..4) |i| {
var new_bits: u128 = decoder.fast_char_to_index[0][source[fast_src_idx + i * 4]];
new_bits |= decoder.fast_char_to_index[1][source[fast_src_idx + 1 + i * 4]];
new_bits |= decoder.fast_char_to_index[2][source[fast_src_idx + 2 + i * 4]];
new_bits |= decoder.fast_char_to_index[3][source[fast_src_idx + 3 + i * 4]];
if ((new_bits & invalid_char_tst) != 0) return error.InvalidCharacter;
bits |= (new_bits << (24 * i));
}
std.mem.writeInt(u128, dest[dest_idx..][0..16], bits, .little);
}
while (fast_src_idx + 4 < source.len and dest_idx + 3 < dest.len) : ({
fast_src_idx += 4;
dest_idx += 3;
}) {
var bits = decoder.fast_char_to_index[0][source[fast_src_idx]];
bits |= decoder.fast_char_to_index[1][source[fast_src_idx + 1]];
bits |= decoder.fast_char_to_index[2][source[fast_src_idx + 2]];
bits |= decoder.fast_char_to_index[3][source[fast_src_idx + 3]];
if ((bits & invalid_char_tst) != 0) return error.InvalidCharacter;
std.mem.writeInt(u32, dest[dest_idx..][0..4], bits, .little);
}
var remaining = source[fast_src_idx..];
for (remaining, fast_src_idx..) |c, src_idx| {
const d = decoder.char_to_index[c];
if (d == invalid_char) {
if (decoder.pad_char == null or c != decoder.pad_char.?) return error.InvalidCharacter;
leftover_idx = src_idx;
break;
}
acc = (acc << 6) + d;
acc_len += 6;
if (acc_len >= 8) {
acc_len -= 8;
dest[dest_idx] = @as(u8, @truncate(acc >> acc_len));
dest_idx += 1;
}
}
if (acc_len > 4 or (acc & (@as(u12, 1) << acc_len) - 1) != 0) {
return error.InvalidPadding;
}
if (leftover_idx == null) return;
var leftover = source[leftover_idx.?..];
if (decoder.pad_char) |pad_char| {
const padding_len = acc_len / 2;
var padding_chars: usize = 0;
for (leftover) |c| {
if (c != pad_char) {
return if (c == Base64Decoder.invalid_char) error.InvalidCharacter else error.InvalidPadding;
}
padding_chars += 1;
}
if (padding_chars != padding_len) return error.InvalidPadding;
}
}
};
pub const Base64DecoderWithIgnore = struct {
decoder: Base64Decoder,
char_is_ignored: [256]bool,
pub fn init(alphabet_chars: [64]u8, pad_char: ?u8, ignore_chars: []const u8) Base64DecoderWithIgnore {
var result = Base64DecoderWithIgnore{
.decoder = Base64Decoder.init(alphabet_chars, pad_char),
.char_is_ignored = [_]bool{false} ** 256,
};
for (ignore_chars) |c| {
assert(result.decoder.char_to_index[c] == Base64Decoder.invalid_char);
assert(!result.char_is_ignored[c]);
assert(result.decoder.pad_char != c);
result.char_is_ignored[c] = true;
}
return result;
}
/// Return the maximum possible decoded size for a given input length - The actual length may be less if the input includes padding.
/// `InvalidPadding` is returned if the input length is not valid.
pub fn calcSizeUpperBound(decoder_with_ignore: *const Base64DecoderWithIgnore, source_len: usize) Error!usize {
var result = source_len / 4 * 3;
if (decoder_with_ignore.decoder.pad_char == null) {
const leftover = source_len % 4;
result += leftover * 3 / 4;
}
return result;
}
/// Invalid characters that are not ignored result in error.InvalidCharacter.
/// Invalid padding results in error.InvalidPadding.
/// Decoding more data than can fit in dest results in error.NoSpaceLeft. See also ::calcSizeUpperBound.
/// Returns the number of bytes written to dest.
pub fn decode(decoder_with_ignore: *const Base64DecoderWithIgnore, dest: []u8, source: []const u8) Error!usize {
const decoder = &decoder_with_ignore.decoder;
var acc: u12 = 0;
var acc_len: u4 = 0;
var dest_idx: usize = 0;
var leftover_idx: ?usize = null;
for (source, 0..) |c, src_idx| {
if (decoder_with_ignore.char_is_ignored[c]) continue;
const d = decoder.char_to_index[c];
if (d == Base64Decoder.invalid_char) {
if (decoder.pad_char == null or c != decoder.pad_char.?) return error.InvalidCharacter;
leftover_idx = src_idx;
break;
}
acc = (acc << 6) + d;
acc_len += 6;
if (acc_len >= 8) {
if (dest_idx == dest.len) return error.NoSpaceLeft;
acc_len -= 8;
dest[dest_idx] = @as(u8, @truncate(acc >> acc_len));
dest_idx += 1;
}
}
if (acc_len > 4 or (acc & (@as(u12, 1) << acc_len) - 1) != 0) {
return error.InvalidPadding;
}
const padding_len = acc_len / 2;
if (leftover_idx == null) {
if (decoder.pad_char != null and padding_len != 0) return error.InvalidPadding;
return dest_idx;
}
var leftover = source[leftover_idx.?..];
if (decoder.pad_char) |pad_char| {
var padding_chars: usize = 0;
for (leftover) |c| {
if (decoder_with_ignore.char_is_ignored[c]) continue;
if (c != pad_char) {
return if (c == Base64Decoder.invalid_char) error.InvalidCharacter else error.InvalidPadding;
}
padding_chars += 1;
}
if (padding_chars != padding_len) return error.InvalidPadding;
}
return dest_idx;
}
};
test "base64" {
if (builtin.zig_backend == .stage2_x86_64) return error.SkipZigTest;
@setEvalBranchQuota(8000);
try testBase64();
try comptime testAllApis(standard, "comptime", "Y29tcHRpbWU=");
}
test "base64 padding dest overflow" {
const input = "foo";
var expect: [128]u8 = undefined;
@memset(&expect, 0);
_ = url_safe.Encoder.encode(expect[0..url_safe.Encoder.calcSize(input.len)], input);
var got: [128]u8 = undefined;
@memset(&got, 0);
_ = url_safe.Encoder.encode(&got, input);
try std.testing.expectEqualSlices(u8, &expect, &got);
}
test "base64 url_safe_no_pad" {
if (builtin.zig_backend == .stage2_x86_64) return error.SkipZigTest;
@setEvalBranchQuota(8000);
try testBase64UrlSafeNoPad();
try comptime testAllApis(url_safe_no_pad, "comptime", "Y29tcHRpbWU");
}
fn testBase64() !void {
const codecs = standard;
try testAllApis(codecs, "", "");
try testAllApis(codecs, "f", "Zg==");
try testAllApis(codecs, "fo", "Zm8=");
try testAllApis(codecs, "foo", "Zm9v");
try testAllApis(codecs, "foob", "Zm9vYg==");
try testAllApis(codecs, "fooba", "Zm9vYmE=");
try testAllApis(codecs, "foobar", "Zm9vYmFy");
try testAllApis(codecs, "foobarfoobarfoo", "Zm9vYmFyZm9vYmFyZm9v");
try testAllApis(codecs, "foobarfoobarfoob", "Zm9vYmFyZm9vYmFyZm9vYg==");
try testAllApis(codecs, "foobarfoobarfooba", "Zm9vYmFyZm9vYmFyZm9vYmE=");
try testAllApis(codecs, "foobarfoobarfoobar", "Zm9vYmFyZm9vYmFyZm9vYmFy");
try testDecodeIgnoreSpace(codecs, "", " ");
try testDecodeIgnoreSpace(codecs, "f", "Z g= =");
try testDecodeIgnoreSpace(codecs, "fo", " Zm8=");
try testDecodeIgnoreSpace(codecs, "foo", "Zm9v ");
try testDecodeIgnoreSpace(codecs, "foob", "Zm9vYg = = ");
try testDecodeIgnoreSpace(codecs, "fooba", "Zm9v YmE=");
try testDecodeIgnoreSpace(codecs, "foobar", " Z m 9 v Y m F y ");
// test getting some api errors
try testError(codecs, "A", error.InvalidPadding);
try testError(codecs, "AA", error.InvalidPadding);
try testError(codecs, "AAA", error.InvalidPadding);
try testError(codecs, "A..A", error.InvalidCharacter);
try testError(codecs, "AA=A", error.InvalidPadding);
try testError(codecs, "AA/=", error.InvalidPadding);
try testError(codecs, "A/==", error.InvalidPadding);
try testError(codecs, "A===", error.InvalidPadding);
try testError(codecs, "====", error.InvalidPadding);
try testError(codecs, "Zm9vYmFyZm9vYmFyA..A", error.InvalidCharacter);
try testError(codecs, "Zm9vYmFyZm9vYmFyAA=A", error.InvalidPadding);
try testError(codecs, "Zm9vYmFyZm9vYmFyAA/=", error.InvalidPadding);
try testError(codecs, "Zm9vYmFyZm9vYmFyA/==", error.InvalidPadding);
try testError(codecs, "Zm9vYmFyZm9vYmFyA===", error.InvalidPadding);
try testError(codecs, "A..AZm9vYmFyZm9vYmFy", error.InvalidCharacter);
try testError(codecs, "Zm9vYmFyZm9vAA=A", error.InvalidPadding);
try testError(codecs, "Zm9vYmFyZm9vAA/=", error.InvalidPadding);
try testError(codecs, "Zm9vYmFyZm9vA/==", error.InvalidPadding);
try testError(codecs, "Zm9vYmFyZm9vA===", error.InvalidPadding);
try testNoSpaceLeftError(codecs, "AA==");
try testNoSpaceLeftError(codecs, "AAA=");
try testNoSpaceLeftError(codecs, "AAAA");
try testNoSpaceLeftError(codecs, "AAAAAA==");
try testFourBytesDestNoSpaceLeftError(codecs, "AAAAAAAAAAAAAAAA");
}
fn testBase64UrlSafeNoPad() !void {
const codecs = url_safe_no_pad;
try testAllApis(codecs, "", "");
try testAllApis(codecs, "f", "Zg");
try testAllApis(codecs, "fo", "Zm8");
try testAllApis(codecs, "foo", "Zm9v");
try testAllApis(codecs, "foob", "Zm9vYg");
try testAllApis(codecs, "fooba", "Zm9vYmE");
try testAllApis(codecs, "foobar", "Zm9vYmFy");
try testAllApis(codecs, "foobarfoobarfoobar", "Zm9vYmFyZm9vYmFyZm9vYmFy");
try testDecodeIgnoreSpace(codecs, "", " ");
try testDecodeIgnoreSpace(codecs, "f", "Z g ");
try testDecodeIgnoreSpace(codecs, "fo", " Zm8");
try testDecodeIgnoreSpace(codecs, "foo", "Zm9v ");
try testDecodeIgnoreSpace(codecs, "foob", "Zm9vYg ");
try testDecodeIgnoreSpace(codecs, "fooba", "Zm9v YmE");
try testDecodeIgnoreSpace(codecs, "foobar", " Z m 9 v Y m F y ");
// test getting some api errors
try testError(codecs, "A", error.InvalidPadding);
try testError(codecs, "AAA=", error.InvalidCharacter);
try testError(codecs, "A..A", error.InvalidCharacter);
try testError(codecs, "AA=A", error.InvalidCharacter);
try testError(codecs, "AA/=", error.InvalidCharacter);
try testError(codecs, "A/==", error.InvalidCharacter);
try testError(codecs, "A===", error.InvalidCharacter);
try testError(codecs, "====", error.InvalidCharacter);
try testError(codecs, "Zm9vYmFyZm9vYmFyA..A", error.InvalidCharacter);
try testError(codecs, "A..AZm9vYmFyZm9vYmFy", error.InvalidCharacter);
try testNoSpaceLeftError(codecs, "AA");
try testNoSpaceLeftError(codecs, "AAA");
try testNoSpaceLeftError(codecs, "AAAA");
try testNoSpaceLeftError(codecs, "AAAAAA");
try testFourBytesDestNoSpaceLeftError(codecs, "AAAAAAAAAAAAAAAA");
}
fn testAllApis(codecs: Codecs, expected_decoded: []const u8, expected_encoded: []const u8) !void {
// Base64Encoder
{
var buffer: [0x100]u8 = undefined;
const encoded = codecs.Encoder.encode(&buffer, expected_decoded);
try testing.expectEqualSlices(u8, expected_encoded, encoded);
}
// Base64Decoder
{
var buffer: [0x100]u8 = undefined;
var decoded = buffer[0..try codecs.Decoder.calcSizeForSlice(expected_encoded)];
try codecs.Decoder.decode(decoded, expected_encoded);
try testing.expectEqualSlices(u8, expected_decoded, decoded);
}
// Base64DecoderWithIgnore
{
const decoder_ignore_nothing = codecs.decoderWithIgnore("");
var buffer: [0x100]u8 = undefined;
var decoded = buffer[0..try decoder_ignore_nothing.calcSizeUpperBound(expected_encoded.len)];
var written = try decoder_ignore_nothing.decode(decoded, expected_encoded);
try testing.expect(written <= decoded.len);
try testing.expectEqualSlices(u8, expected_decoded, decoded[0..written]);
}
}
fn testDecodeIgnoreSpace(codecs: Codecs, expected_decoded: []const u8, encoded: []const u8) !void {
const decoder_ignore_space = codecs.decoderWithIgnore(" ");
var buffer: [0x100]u8 = undefined;
var decoded = buffer[0..try decoder_ignore_space.calcSizeUpperBound(encoded.len)];
var written = try decoder_ignore_space.decode(decoded, encoded);
try testing.expectEqualSlices(u8, expected_decoded, decoded[0..written]);
}
fn testError(codecs: Codecs, encoded: []const u8, expected_err: anyerror) !void {
const decoder_ignore_space = codecs.decoderWithIgnore(" ");
var buffer: [0x100]u8 = undefined;
if (codecs.Decoder.calcSizeForSlice(encoded)) |decoded_size| {
var decoded = buffer[0..decoded_size];
if (codecs.Decoder.decode(decoded, encoded)) |_| {
return error.ExpectedError;
} else |err| if (err != expected_err) return err;
} else |err| if (err != expected_err) return err;
if (decoder_ignore_space.decode(buffer[0..], encoded)) |_| {
return error.ExpectedError;
} else |err| if (err != expected_err) return err;
}
fn testNoSpaceLeftError(codecs: Codecs, encoded: []const u8) !void {
const decoder_ignore_space = codecs.decoderWithIgnore(" ");
var buffer: [0x100]u8 = undefined;
var decoded = buffer[0 .. (try codecs.Decoder.calcSizeForSlice(encoded)) - 1];
if (decoder_ignore_space.decode(decoded, encoded)) |_| {
return error.ExpectedError;
} else |err| if (err != error.NoSpaceLeft) return err;
}
fn testFourBytesDestNoSpaceLeftError(codecs: Codecs, encoded: []const u8) !void {
const decoder_ignore_space = codecs.decoderWithIgnore(" ");
var buffer: [0x100]u8 = undefined;
var decoded = buffer[0..4];
if (decoder_ignore_space.decode(decoded, encoded)) |_| {
return error.ExpectedError;
} else |err| if (err != error.NoSpaceLeft) return err;
}